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diff --git a/docs/src/index.md b/docs/src/index.md
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 ```@contents
 ```
 
-ModelReduction.jl is (write here)
+ModelReduction.jl is a Julia package to perform model reduction methods for i.e. multibody dynamics problems. The packcage includes model order reduction methods such as the Guyan reduction and the Craig-Bampton method.
 
-## Installing and testing package
+Reducing the sizes of stiffness and mass matrices of the model will greatly decrease the computation resources needed when performing dynamic analyses.
+
+ModelReduction.jl is a part of JuliaFEM. All codes are MIT licensed.
+
+## Installing and testing the package
+
+Download and unzip the packge files into your Julia folder and then install the package the same way other Julia packages are installed.
+
+```julia
+julia> Pkg.add("ModelReduction")
+
+```
+
+Test the package with ```Pkg.test``` etc.
+
+```julia
+julia> Pkg.test("ModelReduction")
+
+```
 
-( write here how to install and test package )
 
 ## Usage example
 
-( demonstrate here how to use package, simple example )
+This example demonstrates how to use the Craig-Bampton method function.
+
+Problem setup:
+
+```julia
+K =
+[2 -1 0 0;
+-1 2 -1 0;
+ 0 -1 2 -1;
+ 0 0 -1 1]
+
+M =
+[2 0 0 0;
+ 0 2 0 0;
+ 0 0 2 0;
+ 0 0 0 1]
+
+r = [4]
+l = [1, 2, 3]
+n = 1
+
+```
+K = original stiffness matrix, M = original mass matrix, r = retained DOF:s, l = internal DOF:s, n = the number of the internal modes to keep.
+Calculate the reduced mass and stiffness matrices Mred and Kred.
+
+```julia
+craig_bampton(K, M, r, l, n)
+
+# output
+
+Mred, Kred = ([2.75 -1.20711; -1.20711 1.0], [0.25 0.0; 0.0 0.292893])
+
+```
+
 
 ## Contributing
 
-( write here how to contribute to package )
+
+
+Have a new great idea and want to share it with the open source community? 
+From [here](https://github.com/JuliaLang/julia/blob/master/CONTRIBUTING.md)
+and [here](https://juliadocs.github.io/Documenter.jl/stable/man/contributing/)
+you can look for coding styles. [Here](https://docs.julialang.org/en/stable/manual/packages/#Making-changes-to-an-existing-package-1) it is explained how to contribute to 
+open source project, in general.
+
diff --git a/docs/src/theory.md b/docs/src/theory.md
@@ -1,13 +1,193 @@
 # Theory
 
-( write here what is the theory behing package )
+The Craig-Bampton method is a dynamic reduction technique that reduces
+the mass and stiffness matrices of the model by expressing the boundary
+modes in physical coordinates and the elastic modes in modal coordinates.
 
-# References
+The equation of motion is:
+
+```math
+\begin{equation}
+\boldsymbol{M}\ddot{\boldsymbol{u}}+\boldsymbol{K}\boldsymbol{u}=\boldsymbol{f}
+\end{equation}
+```
+
+The matrices are partitioned into boundary nodes R and the independent
+elastic nodes L:
+
+```math
+\begin{equation}
+\boldsymbol{u}=\begin{bmatrix}\boldsymbol{u}_{\mathrm{R}}\\
+\boldsymbol{u}_{\mathrm{L}}
+\end{bmatrix}
+\end{equation}
+```
+
+Equation (1) becomes:
+
+```math
+\begin{equation}
+\begin{bmatrix}\boldsymbol{M}_{\mathrm{RR}} & \boldsymbol{M}_{\mathrm{\mathrm{R}L}}\\
+\boldsymbol{M}_{\mathrm{RR}} & \boldsymbol{M}_{\mathrm{LL}}
+\end{bmatrix}\begin{bmatrix}\ddot{\boldsymbol{u}}_{\mathrm{R}}\\
+\ddot{\boldsymbol{u}}_{\mathrm{L}}
+\end{bmatrix}+\begin{bmatrix}\boldsymbol{K}_{\mathrm{RR}} & \boldsymbol{K}_{\mathrm{RL}}\\
+\boldsymbol{K}_{\mathrm{LR}} & \boldsymbol{K}_{\mathrm{LL}}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{u}_{\mathrm{R}}\\
+\boldsymbol{u}_{\mathrm{L}}
+\end{bmatrix}=\boldsymbol{f}
+\end{equation}
+```
+
+The degrees of freedom are are transformed to hybrid coordinates
+
+```math
+\begin{equation}
+\begin{bmatrix}\boldsymbol{u}_{\mathrm{R}}\\
+\boldsymbol{u}_{\mathrm{L}}
+\end{bmatrix}=\begin{bmatrix}\boldsymbol{I} & \boldsymbol{0}\\
+\boldsymbol{X}_{\mathrm{R}} & \boldsymbol{X}_{\mathrm{L}}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{u}_{\mathrm{R}}\\
+\boldsymbol{q}_{\mathrm{m}}
+\end{bmatrix}
+\end{equation}
+```
+
+Equation (1) can be rewritten as
+
+```math
+\begin{equation}
+\begin{bmatrix}\boldsymbol{M}_{\mathrm{RR}} & \boldsymbol{M}_{\mathrm{\mathrm{R}L}}\\
+\boldsymbol{M}_{\mathrm{RR}} & \boldsymbol{M}_{\mathrm{LL}}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{I} & \boldsymbol{0}\\
+\boldsymbol{X}_{\mathrm{R}} & \boldsymbol{X}_{\mathrm{L}}
+\end{bmatrix}\begin{bmatrix}\ddot{\boldsymbol{u}}_{\mathrm{R}}\\
+\ddot{\boldsymbol{q}}_{\mathrm{m}}
+\end{bmatrix}+\begin{bmatrix}\boldsymbol{K}_{\mathrm{RR}} & \boldsymbol{K}_{\mathrm{RL}}\\
+\boldsymbol{K}_{\mathrm{LR}} & \boldsymbol{K}_{\mathrm{LL}}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{I} & \boldsymbol{0}\\
+\boldsymbol{X}_{\mathrm{R}} & \boldsymbol{X}_{\mathrm{L}}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{u}_{\mathrm{R}}\\
+\boldsymbol{q}_{\mathrm{m}}
+\end{bmatrix}=\begin{bmatrix}\boldsymbol{f}_{\mathrm{R}}\\
+\boldsymbol{0}
+\end{bmatrix}
+\end{equation}
+```
+Equation (1) reduces to
+
+```math
+\begin{equation}
+\boldsymbol{K}_{\mathrm{LR}}\boldsymbol{K}_{\mathrm{LR}}\boldsymbol{u}_{\mathrm{R}}+\boldsymbol{K}_{\mathrm{LL}}\boldsymbol{u}_{\mathrm{L}}
+\end{equation}
+```
+
+The internal degrees of freedom can be expressed as
+
+```math
+\begin{equation}
+\boldsymbol{u}_{\mathrm{L}}=-\boldsymbol{K}_{\mathrm{LL}}^{-1}\boldsymbol{K}_{\mathrm{LR}}\boldsymbol{u}_{\mathrm{R}}=\boldsymbol{X}_{\mathrm{R}}\boldsymbol{u}_{\mathrm{R}}
+\end{equation}
+```
+
+where
+
+```math
+\begin{equation}
+\boldsymbol{X}_{\mathrm{R}}=-\boldsymbol{K}_{\mathrm{LL}}^{-1}\boldsymbol{K}_{\mathrm{LR}}
+\end{equation}
+```
 
-( add here the list of references, if any, I leave the list below as example )
+To determine \mathit{\boldsymbol{X}}_{\mathrm{L}} the retained degrees of freedom are fixed. The equation of motion reduces to
+
+```math
+\begin{equation}
+\boldsymbol{M}_{\mathrm{LL}}\ddot{\boldsymbol{u}}_{\mathrm{L}}+\boldsymbol{K}_{\mathrm{LL}}\boldsymbol{u}_{\mathrm{L}}=0
+\end{equation}
+```
+
+By assuming harmonic response and substituting the coordinate transformation (4)
+
+```math
+\begin{equation}
+(-\omega^{2}\boldsymbol{M}_{\mathrm{LL}}+\boldsymbol{K}_{\mathrm{LL}})\boldsymbol{X}_{\mathrm{L}}\boldsymbol{q}_{\mathrm{m}}e^{i\omega t}=0
+\end{equation}
+```
+
+The eigenvectors can be normalized:
+
+```math
+\begin{equation}
+\boldsymbol{X}_{\mathrm{L}}^{\mathrm{T}}\boldsymbol{M}_{\mathrm{LL}}\boldsymbol{X}_{\mathrm{L}}=\boldsymbol{I}
+\end{equation}
+```
+
+```math
+\begin{equation}
+\boldsymbol{X}_{\mathrm{L}}^{\mathrm{T}}\boldsymbol{K}_{\mathrm{LL}}\boldsymbol{X}_{\mathrm{L}}=\boldsymbol{\Lambda}
+\end{equation}
+```
+
+Since $\boldsymbol{X}$$_{\mathrm{R}}$ in (9) contains $\boldsymbol{K}$$_{\mathrm{LL}}^{-1}$,
+an inverse of $\boldsymbol{K}$$_{\mathrm{LL}}$, determining it will
+require lots of computing resources. This can be avoided by determining
+the $\boldsymbol{K}$$_{\mathrm{LL}}$ inverse as follows.
+
+```math
+\begin{equation}
+-\boldsymbol{K}_{\mathrm{LL}}^{-1}=\boldsymbol{X}_{\mathrm{L}}\boldsymbol{\Lambda}^{-1}\boldsymbol{X}_{\mathrm{L}}^{\mathrm{T}}
+\end{equation}
+```
+
+In order to get the dynamic equations of the system, equation (6) is multiplied with the coordination transformation matrix.
+
+```math
+\begin{multline}
+\begin{bmatrix}\boldsymbol{I} & \boldsymbol{X}_{\mathrm{R}}^{\mathrm{T}}\\
+\boldsymbol{0} & \boldsymbol{X}_{\mathrm{L}}^{\mathrm{T}}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{M}_{\mathrm{RR}} & \boldsymbol{M}_{\mathrm{\mathrm{R}L}}\\
+\boldsymbol{M}_{\mathrm{LR}} & \boldsymbol{M}_{\mathrm{LL}}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{I} & \boldsymbol{0}\\
+\boldsymbol{X}_{\mathrm{R}} & \boldsymbol{X}_{\mathrm{L}}
+\end{bmatrix}\begin{bmatrix}\ddot{\boldsymbol{u}}_{\mathrm{R}}\\
+\ddot{\boldsymbol{q}}_{\mathrm{m}}
+\end{bmatrix}\\
++\begin{bmatrix}\boldsymbol{I} & \boldsymbol{X}_{\mathrm{R}}^{\mathrm{T}}\\
+\boldsymbol{0} & \boldsymbol{X}_{\mathrm{L}}^{\mathrm{T}}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{K}_{\mathrm{RR}} & \boldsymbol{K}_{\mathrm{RL}}\\
+\boldsymbol{K}_{\mathrm{LR}} & \boldsymbol{K}_{\mathrm{LL}}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{I} & \boldsymbol{0}\\
+\boldsymbol{X}_{\mathrm{R}} & \boldsymbol{X}_{\mathrm{L}}
+\end{bmatrix}\begin{bmatrix}\mathbf{\mathit{\boldsymbol{u}}}_{\mathrm{R}}\\
+\boldsymbol{q}_{\mathrm{m}}
+\end{bmatrix}=\begin{bmatrix}\boldsymbol{I} & \boldsymbol{X}_{\mathrm{R}}^{\mathrm{T}}\\
+\boldsymbol{0} & \boldsymbol{X}_{\mathrm{L}}^{\mathrm{T}}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{f}_{\mathrm{R}}\\
+\boldsymbol{0}
+\end{bmatrix}
+\end{multline}
+```
+
+By simplifying the equation of motion (1) becomes
+
+```math
+\begin{multline}
+\begin{bmatrix}\boldsymbol{M}_{\mathrm{RR}}+\boldsymbol{X}_{\mathrm{R}}^{\mathrm{T}}\boldsymbol{M}_{\mathrm{LR}}+\boldsymbol{X}_{\mathrm{R}}^{\mathrm{T}}\boldsymbol{M}_{\mathrm{LL}}\boldsymbol{X}_{\mathrm{R}} & \boldsymbol{M}_{\mathrm{\mathrm{R}L}}\boldsymbol{X}_{\mathrm{L}}+\boldsymbol{X}_{\mathrm{R}}^{\mathrm{T}}\boldsymbol{M}_{\mathrm{LL}}\boldsymbol{X}_{\mathrm{L}}\\
+\boldsymbol{X}_{\mathrm{L}}^{\mathrm{T}}\boldsymbol{M}_{\mathrm{LR}}+\boldsymbol{X}_{\mathrm{L}}^{\mathrm{T}}\boldsymbol{M}_{\mathrm{LL}}\boldsymbol{X}_{\mathrm{R}} & \boldsymbol{I}
+\end{bmatrix}\begin{bmatrix}\ddot{\boldsymbol{u}}_{\mathrm{R}}\\
+\ddot{\boldsymbol{q}}_{\mathrm{m}}
+\end{bmatrix}\\
++\begin{bmatrix}\boldsymbol{K}_{\mathrm{RR}}+\boldsymbol{K}_{\mathrm{RL}}\boldsymbol{X}_{\mathrm{R}} & \boldsymbol{0}\\
+\boldsymbol{0} & \boldsymbol{\Lambda}
+\end{bmatrix}\begin{bmatrix}\boldsymbol{u}_{\mathrm{R}}\\
+\boldsymbol{q}_{\mathrm{m}}
+\end{bmatrix}=\begin{bmatrix}\boldsymbol{f}_{\mathrm{R}}\\
+\boldsymbol{0}
+\end{bmatrix}
+\end{multline}
+```
+
+# References
 
-- Wikipedia contributors. "Mortar methods." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia.
-- Maday, Yvon, Cathy Mavriplis, and Anthony Patera. "Nonconforming mortar element methods: Application to spectral discretizations." (1988).
-- Yang, Bin, Tod A. Laursen, and Xiaonong Meng. "Two dimensional mortar contact methods for large deformation frictional sliding." International journal for numerical methods in engineering 62.9 (2005): 1183-1225.
-- Yang, Bin, and Tod A. Laursen. "A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulations." Computational Mechanics 41.2 (2008): 189-205.
-- Wohlmuth, Barbara I. "A mortar finite element method using dual spaces for the Lagrange multiplier." SIAM journal on numerical analysis 38.3 (2000): 989-1012.
+- Qu, Zu-Qing. Model Order Reduction Techniques (2004). p. 322 - 329.
+- Young, John T. Prime on the Craig-Bampton Method (2000). p. 5 - 17.