diff --git a/README.md b/README.md
index 4b87c75..bbcd5de 100644
--- a/README.md
+++ b/README.md
@@ -17,83 +17,324 @@ Main characteristics:
 
 Implementation wise, it is a tiny (1300 LOC) library without any external dependencies.
 
-## Comparison with the Svelte stores
+## Installation
 
-Tansu is designed to be and to remain fully compatible with Svelte. Nevertheless, it brings several improvements:
+You can add Tansu to your project by installing the `@amadeus-it-group/tansu` package using your favorite package manager, ex.:
 
-### Tansu works well with the Angular ecosystem
+* `yarn add @amadeus-it-group/tansu`
+* `npm install @amadeus-it-group/tansu`
 
-* works with the standard `async` pipe out of the box
-* stores can be registered in the dependency injection (DI) container at any level (module or component injector)
-* stores can be used easily with rxjs because they implement the `InteropObservable` interface
-* conversely, rxjs observables (or any object implementing the `InteropObservable` interface) can easily be used with Tansu (e.g. in Tansu `computed` or `derived`).
+## Usage
 
-### A computed function is available
+Check out the [Tansu API documentation](https://amadeusitgroup.github.io/tansu/).
 
-With Svelte `derived` function, it is mandatory to provide explicitly a static list of dependencies when the store is created, for example:
+The functional part of the API to manage your reactive state can be categorized into three distinct groups:
+
+  - Base store: `writable`
+  - Computed stores: `derived`, `computed`, `readable`
+  - Utilities: `batch`, `asReadable`, `asWritable`
+
+### writable
+
+[api documentation](https://amadeusitgroup.github.io/tansu/functions/writable.html)
+
+**Writable: A Fundamental Building Block**
+
+
+A `writable` serves as the foundational element of a "store" – a container designed to encapsulate a value, enabling observation and modification of its state. You can change the internal value using the `set` or `update` methods.
+
+To receive notifications whenever the value undergoes a change, the `subscribe()` method, paired with a callback function, can be employed.
+
+#### Basic usage
 
 ```typescript
-import {writable, derived} from 'svelte/store';
+import {writable} from "@amadeus-it-group/tansu";
+const value$ = writable(0);
 
-const quantity = writable(2);
-const unitPrice = writable(10);
-const totalPrice = derived([quantity, unitPrice], ([quantity, unitPrice]) => {
-  console.log("computing the total price");
-  return quantity > 0 ? quantity * unitPrice : 0
+const unsubscribe = values$.subscribe((value) => {
+  console.log(`value = ${value}`);
 });
-totalPrice.subscribe((totalPrice) => console.log(totalPrice)); // logs any change to totalPrice
-quantity.set(0);
-unitPrice.set(20);
+
+value$.set(1);
+value$.update((value) => value + 1);
 ```
 
-The output of this example will be:
+output:
 
 ```text
-computing the total price
-20
-computing the total price
-0
-computing the total price
+  value = 0
+  value = 1
+  value = 2
 ```
 
-Note that even when the quantity is 0, the total is recomputed when the unit price changes.
+#### Setup and teardown
 
-In Tansu, while the same [derived](https://amadeusitgroup.github.io/tansu/functions/derived.html) function is still available, the [computed](https://amadeusitgroup.github.io/tansu/functions/computed.html) function is also available, with which it is only necessary to provide a function, and the list of dependencies is detected automatically and dynamically:
+The writable's second parameter allows for receiving notifications when at least one subscriber subscribes or when there are no more subscribers.
 
 ```typescript
-import {writable, computed} from '@amadeus-it-group/tansu';
+import {writable} from "@amadeus-it-group/tansu";
+
+const value$ = writable(0, () => {
+  console.log('At least one subscriber');
 
-const quantity = writable(2);
-const unitPrice = writable(10);
-const totalPrice = computed(() => {
-  console.log("computing the total price");
-  return quantity() > 0 ? quantity() * unitPrice() : 0
+  return () => {
+    console.log('No more subscriber');
+  }
+});
+
+const unsubscribe = values$.subscribe((value) => {
+  console.log(`value = ${value}`);
 });
-totalPrice.subscribe((totalPrice) => console.log(totalPrice)); // logs any change to totalPrice
-quantity.set(0);
-unitPrice.set(20);
+
+value$.set(1);
+unsubscribe();
+```
+
+output:
+
+```text
+  At least one subscriber
+  value = 0
+  value = 1
+  No more subscriber
 ```
 
-Note that every store created with `store = writable(value)` is a function that returns the value of the store. It is equivalent to `get(store)`.
-When getting the value of a store (either by calling the store as a function or by using `get`) from a reactive context (such as the one created by `computed`) the dependency on that store is recorded and any change to that store will trigger a recomputation.
+### derived
+
+[api documentation](https://amadeusitgroup.github.io/tansu/functions/derived.html)
+
+A `derived` store calculates its value based on one or more other stores provided as parameters.
+Since its value is derived from other stores, it is a read-only store and does not have any `set` or `update` methods.
+
+#### Single store
+
+```typescript
+import {writable, derived} from "@amadeus-it-group/tansu";
+
+const value$ = writable(1);
+const double$ = derived(value$, (value) => value * 2);
+
+double$.subscribe((double) => console.log('Double value', double));
+value$.set(2);
+```
+
+output:
+
+```text
+Double value 2
+Double value 4
+```
+
+#### Multiple stores
+
+```typescript
+import {writable, derived} from "@amadeus-it-group/tansu";
+
+const a$ = writable(1);
+const b$ = writable(1);
+const sum$ = derived([a$, b$], ([a, b]) => a + b);
+
+sum$.subscribe((sum) => console.log('Sum', sum));
+a$.set(2);
+```
+
+output:
+
+```text
+Sum 2
+Sum 3
+```
+
+#### Asynchronous set
+
+A `derived` can directly manipulate its value using the set method instead of relying on the returned value of the provided function.
+This flexibility allows you to manage asynchronous operations or apply filtering logic before updating the observable's value.
+
+```typescript
+import {writable, derived} from "@amadeus-it-group/tansu";
+
+const a$ = writable(0);
+const asynchronousDouble$ = derived(a$, (a, set) => {
+  const plannedLater = setTimeout(() => set(a * 2));
+  return () => {
+    // This clean-up function is called if there is no listener anymore,
+    // or if the value of a$ changed
+    // In this case, the function passed to setTimeout should not be called
+    // (if it was not called already)
+    clearTimeout(plannedLater);
+  };
+}, -1);
+
+const evenOnly$ = derived(a$, (a, set) => {
+  if (a % 2 === 0) {
+      set(a);
+  }
+}, <number | undefined>undefined);
+
+asynchronousDouble$.subscribe((double) => console.log('Double (asynchronous)', double));
+evenOnly$.subscribe((value) => console.log('Even', value));
+
+a$.set(1);
+a$.set(2);
+```
+
+output:
+
+```text
+Double (asynchronous) -1
+Even 0
+Even 2
+Double (asynchronous) 4
+```
+
+
+### computed
+
+[api documentation](https://amadeusitgroup.github.io/tansu/functions/computed.html)
+
+A `computed` store is another variant of a derived store, with the following characteristics:
+
+  - **Implicit Dependencies:** Unlike in a derived store, there is no requirement to explicitly declare dependencies.
+
+  - **Dynamic Dependency Listening:** Dependencies are determined based on their usage. This implies that a dependency not actively used is not automatically "listened" to, optimizing resource utilization.
+
+#### Switch map
+
+This capability to subscribe/unsubscribe to the dependency allows to create switch maps in a natural way.
+
+```typescript
+import {writable, computed} from "@amadeus-it-group/tansu";
+
+const switchToA$ = writable(true);
+const a$ = writable(1);
+const b$ = writable(0);
+
+const computedValue$ = computed(() => {
+  if (switchToA$()) {
+    console.log('Return a$');
+    return a$();
+  } else {
+    console.log('Return b$');
+    return b$();
+  }
+});
+
+computedValue$.subscribe((value) => console.log('Computed value:', value));
+a$.set(2);
+switchToA$.set(false);
+a$.set(3);
+a$.set(4);
+switchToA$.set(true);
+
+```
 
-The output of this example will be:
+output:
 
 ```text
-computing the total price
-20
-computing the total price
-0
+Return a$
+Computed value: 1
+Return a$
+Computed value: 2
+Return b$
+Computed value: 0
+Return a$
+Computed value: 4
 ```
 
-Note that when the quantity is 0, changes to the unit price no longer trigger an update of the total price because the list of dependencies is dynamic (and `unitPrice()` is not called if `quantity()` is `0`).
+When `switchToA$.set(false)` is called, the subscription to `a$` is canceled, which means that subsequent changes to `a$` will no longer trigger the calculation., which is only performed again when switchToA$ is set back to true.
 
-### A batch function is available
+### readable
 
-Depending on multiple stores can lead to some issues. Let's have a look at the following example:
+[api documentation](https://amadeusitgroup.github.io/tansu/functions/readable.html)
+
+Similar to Svelte stores, this function generates a store where the value cannot be externally modified.
+
+```typescript
+import {readable} from '@amadeus-it-group/tansu';
+
+const time = readable(new Date(), (set) => {
+  const interval = setInterval(() => {
+    set(new Date());
+  }, 1000);
+
+  return () => clearInterval(interval);
+});
+```
+
+### derived vs computed
+
+While derived and computed may appear similar, they exhibit distinct characteristics that can significantly impact effectiveness based on use-cases:
+
+- **Declaration of Dependencies:**
+  - `computed`: No explicit declaration of dependencies is required, providing more flexibility in code composition.
+  - `derived`: Requires explicit declaration of dependencies.
+
+- **Performance:**
+  - `computed`: Better performance by re-running the function only based on changes in the stores involved in the last run.
+  - `derived`: Re-run the function each time a dependent store changes.
+
+- **Asynchronous State:**
+  - `computed`: Unable to manage asynchronous state.
+  - `derived`: Can handle asynchronous state with the `set` method.
+
+- **Skipping Value Emission:**
+  - `computed`: Does not provide a mechanism to skip emitting values.
+  - `derived`: Allows skipping the emission of values by choosing not to call the provided `set` method.
+
+- **Setup and Teardown:**
+  - `computed`: Lacks explicit setup and teardown methods.
+  - `derived`: Supports setup and teardown methods, allowing actions such as adding or removing DOM listeners.
+  - When the last listener unsubscribes and then subscribes again, the derived function is rerun due to its setup-teardown functionality. In contrast, a computed provides the last value without recomputing if dependencies haven't changed in the meantime.
+
+While `computed` feels more intuitive in many use-cases, `derived` excels in scenarios where `computed` falls short, particularly in managing asynchronous state and providing more granular control over value emissions.
+
+Carefully choosing between them based on specific requirements enhances the effectiveness of state management in your application.
+
+### Getting the value
+
+There are three ways for getting the value of a store:
 
 ```typescript
-import {writable, derived} from 'svelte/store';
+import {writable, get} from "@amadeus-it-group/tansu";
+
+const count$ = writable(1);
+const unsubscribe = count$.subscribe((count) => {
+  // Will be called with the updated value synchronously first, then each time count$ changes.
+  // `unsubscribe` must be called to prevent future calls.
+  console.log(count);
+});
+
+// A store is also a function that you can call to get the instant value.
+console.log(count$());
+
+// Equivalent to
+console.log(get(count$));
+```
+
+> [!NOTE]
+> Getting the instant value implies the subscription and unsubription on the store:
+>   - It can be important to know in case of setup/teardown functions.
+>   - In the same scope, prefer to store the value once in a local variable instead of calling `store$()` several times.
+>
+> When called inside a reactive context (i.e. inside a computed), getting the value serves to know and "listen" the dependent stores.
+
+
+### batch
+
+[api documentation](https://amadeusitgroup.github.io/tansu/functions/batch.html)
+
+Contrary to other libraries like Angular with signals or Svelte with runes, where the callback of a subscription is executed asynchronously (usually referenced as an "effect"), we have maintained the constraint of synchronicity between the store changes and their subscriptions in Tansu.
+
+While it is acceptable for these frameworks to defer these calls since their goals are well-known in advance (to optimize their final rendering), this is not the case for Tansu, where the goal is to be adaptable to any situation.
+
+The problem with synchronous subscriptions is that it can create "glitches". Subscribers and computed store callbacks that are run too many times can create incorrect intermediate values.
+
+Svelte stores resolved the [diamond dependency issue](https://github.com/sveltejs/svelte/pull/2955), but it does not match all the use-cases.
+
+Let's have a look at the following example:
+
+```typescript
+import {writable, derived} from '@amadeus-it-group/tansu';
 
 const firstName = writable('Arsène');
 const lastName = writable('Lupin');
@@ -104,7 +345,7 @@ lastName.set('Holmes');
 console.log('Process end');
 ```
 
-The output of this example will be:
+output:
 
 ```text
 Arsène Lupin
@@ -115,7 +356,7 @@ Process end
 
 The fullName store successively went through different states, including an inconsistent one, as `Sherlock Lupin` does not exist! Even if it can be seen as just an intermediate state, it is **fundamental** for a state management to only manage consistent data in order to prevent issues and optimize the code.
 
-In Tansu, the [batch function](https://amadeusitgroup.github.io/tansu/functions/batch.html) is available to defer **synchronously** (another important point) the derived (or computed) calculation and solve all kind of multiple dependencies issues.
+In Tansu, the `batch` is available to defer **synchronously** the subscribers calls, and de facto the dependent `derived` or `computed` calculation to solve all kind of multiple dependencies issues.
 
 The previous example is resolved this way:
 
@@ -135,22 +376,103 @@ batch(() => {
 console.log('Process end');
 ```
 
-With the following output:
+output:
 
 ```text
 Arsène Lupin
 Sherlock Holmes
 Process end
 ```
+> [!NOTE]
+> - Retrieving the immediate value of a store (using any of the three methods mentioned earlier: calling `subscribe` with a subscriber that will be called with the value synchronously, using `get` or calling the store as a function) always provides the value based on the up-to-date values of all dependent stores (even if this requires re-computations of a computed or a derived inside the batch)
+> - all calls to subscribers (excluding the first synchronous call during the subscribe process) are deferred until the end of the batch
+> - if a subscriber has already been notified of a new value inside the batch (for example, when it is a new subscriber registered within the batch), it won't be notified again at the end of the batch if the value remains unchanged. Subscribers are invoked only when the store's value has changed since their last call.
+> - `batch` can be called inside `batch`. The subscriber calls are performed at the end of the first batch, synchronously.
 
-## Installation
 
-You can add Tansu to your project by installing the `@amadeus-it-group/tansu` package using your favorite package manager, ex.:
+### asReadable
 
-* `yarn add @amadeus-it-group/tansu`
-* `npm install @amadeus-it-group/tansu`
+[api documentation](https://amadeusitgroup.github.io/tansu/functions/asReadable.html)
 
-## Usage
+`asReadable` returns a new store that exposes only the essential elements needed for subscribing to the store. It also includes any extra methods passed as parameters.
+
+This is useful and widely used to compose a custom store:
+
+  - The first parameter is the writable store,
+  - The second parameter is an object to extend the readable store returned.
+
+```typescript
+import {writable, asReadable} from "@amadeus-it-group/tansu";
+
+function createCounter(initialValue: number) {
+  const store$ = writable(initialValue);
+
+  return asReadable(store$, {
+    increment: () => store$.update((value) => value + 1),
+    decrement: () => store$.update((value) => value - 1),
+    reset: () => store$.set(initialValue)
+  });
+}
+
+const counter$ = createCounter(0);
+
+counter$.subscribe((value) => console.log('Value: ', value));
+
+counter$.increment();
+counter$.reset();
+counter$.set(2); // Error, set does not exist
+```
+output:
+```text
+Value: 0
+Value: 1
+Value: 0
+(Error thrown !)
+```
+
+### asWritable
+
+[api documentation](https://amadeusitgroup.github.io/tansu/functions/asWritable.html)
+
+`asWritable` is almost the same as an `asReadable`, with the key difference being its implementation of the [WritableSignal](https://amadeusitgroup.github.io/tansu/interfaces/WritableSignal.html) interface.
+
+It's useful when you want to connect your computed store to the original one, or implement a custom `set` method. The `set` method can be passed directly in the second parameter or within an object, similar to the usage in `asReadable`.
+
+For example:
+
+```typescript
+import {writable, asWritable} from "@amadeus-it-group/tansu";
+
+const number$ = writable(1);
+const double$ = asWritable(number$, (doubleNumber) => {
+  number$.set(doubleNumber / 2);
+});
+
+/* equivalent to:
+  const double$ = asWritable(number$, {
+    set: (doubleNumber) => number$.set(doubleNumber / 2)
+  });
+*/
+
+double$.subscribe((value) => console.log('Value: ', value));
+
+double$.set(2); // Nothing is triggered here, as number$ is already set with 1
+double$.set(4);
+
+```
+output:
+```text
+Value: 2
+Value: 4
+```
+
+## Integration in frameworks
+
+### Tansu works well with the Svelte framework
+
+Tansu is designed to be and to remain fully compatible with Svelte.
+
+### Tansu works well with the Angular ecosystem
 
 Here is an example of an Angular component using a Tansu store:
 
@@ -198,9 +520,12 @@ export class App {
 }
 ```
 
-While being fairly minimal, this example demonstrates most of the Tansu APIs.
+While being fairly minimal, this example demonstrates most of the Tansu APIs with Angular.
 
-Check the [documentation](http://amadeusitgroup.github.io/tansu/) for the complete API and more usage examples.
+* works with the standard `async` pipe out of the box
+* stores can be registered in the dependency injection (DI) container at any level (module or component injector)
+* stores can be used easily with rxjs because they implement the `InteropObservable` interface
+* conversely, rxjs observables (or any object implementing the `InteropObservable` interface) can easily be used with Tansu (e.g. in Tansu `computed` or `derived`).
 
 ## Contributing to the project