diff --git a/README.md b/README.md
index 63afd4eccd0d3b1f3203994dcdd5ed45503c03c0..8822edb7dd58dcae2c74d86f01e58e774a121f1e 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
 # Alligators-python
 
-
+<img align="right" width="200" height="100" src="https://i.imgur.com/C5MWF5V.png">
 
 ## About the project
 
@@ -9,7 +9,7 @@ The main goal of the program is to generate the result of the beta_reduction of
 ## Table of contents
 
 
-<!-- TOC -->- [The structures](#structures)<br />    - [What to install](#needs)<br />    - [How to install](#how)<br />    - [Usage](#utilisation)<br />    - [Parsing syntax ](#parse)<br />    - [Documentation](#docu)<br />    - [Contribution](#contri)<br /> <!-- /TOC -->
+<!-- TOC -->- [The structures](#structures)<br />    - [What to install](#needs)<br />    - [How to install](#how)<br />    - [Usage](#utilisation)<br />    - [Parsing syntax ](#parse)<br />    - [Documentation](#docu)<br />    - [Project status and Contribution](#status)<br /> <!-- /TOC -->
 
 ## Structures <a name="structures"></a>
 
@@ -30,7 +30,7 @@ The JPEG images are already created, to build the image of a lambda term, we jus
 ## How to install <a name="how"></a>
 
 - To install the needed tools, you have to use the following command:<br />
-pip install requirements.txt
+ `pip: -r requirements.txt`
 
 ## Usage <a name="utilisation"></a>
 The program is very simple to use, these are some advices once we run the code: <br />
@@ -38,51 +38,45 @@ The program is very simple to use, these are some advices once we run the code:
 2. The lambda term that is given as an input has to respect some syntactic rules, you can find the rules in the section parsing syntax.
 3. When you choose an option in the menu, the images that could have been generated are stocked in a temporary directory which you are free to save or delete at the end.
 
+## Parsing Syntax <a name="parse"></a>
+In order to parse a lambda term, we have to respect some rules:<br />
+1. The lambda term has to be written in a single line.<br />
+2. Represent the lambda by a hashtag '#'<br />
+3. For the variable, the name of the variables cannnot contain spaces or it wont be considered a variable (it would be considered an application)<br />
+4. For the abstraction, the input has to be written between the hashtag '#' and the point '.' which seperates the input from the output, then WITHOUT SPACE directly after the dot the output of the term should be written<br />
+5. For the application, the first term has to be written between parantheses only if it is not a variable and then a SPACE seperates the first term from the second, which should be written between parantheses only if it is an application<br />
+EXAMPLES:<br />
+` λx.x ---> #x.x`<br />
+`λx.x λy.y ---> (#x.x) #y.y`     ( NOT `#x.(x #y.y)` )<br />
+`λf.(λx.(f(x x)))λx.(f(x x)) ---> #f.(#x.(#f.(x x)))c#f.(#x.(#f.(x x)))`
+
+##  Documentation <a name="docu"></a>
+<a href='https://en.wikipedia.org/wiki/Lambda_calculus'>WikiPedia: Lambda Calculus<a>
+<a href='https://brilliant.org/wiki/lambda-calculus/'>Brilliant: Lambda Calculus<a>
+<a href='https://mpsib-camille-guerin.pagesperso-orange.fr/Python/Lambda/Lambda2/Lambda2.pdf'>MPSIB-CAMILLE-GUERIN: Lambda Calculus<a>
 ***
 
-# Editing this README
-
-When you're ready to make this README your own, just edit this file and use the handy template below (or feel free to structure it however you want - this is just a starting point!).  Thank you to [makeareadme.com](https://www.makeareadme.com/) for this template.
-
-## Suggestions for a good README
-Every project is different, so consider which of these sections apply to yours. The sections used in the template are suggestions for most open source projects. Also keep in mind that while a README can be too long and detailed, too long is better than too short. If you think your README is too long, consider utilizing another form of documentation rather than cutting out information.
-
-## Name
-Choose a self-explaining name for your project.
-
-## Description
-Let people know what your project can do specifically. Provide context and add a link to any reference visitors might be unfamiliar with. A list of Features or a Background subsection can also be added here. If there are alternatives to your project, this is a good place to list differentiating factors.
-
-## Badges
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-
-## Visuals
-Depending on what you are making, it can be a good idea to include screenshots or even a video (you'll frequently see GIFs rather than actual videos). Tools like ttygif can help, but check out Asciinema for a more sophisticated method.
-
-## Installation
-Within a particular ecosystem, there may be a common way of installing things, such as using Yarn, NuGet, or Homebrew. However, consider the possibility that whoever is reading your README is a novice and would like more guidance. Listing specific steps helps remove ambiguity and gets people to using your project as quickly as possible. If it only runs in a specific context like a particular programming language version or operating system or has dependencies that have to be installed manually, also add a Requirements subsection.
 
-## Usage
-Use examples liberally, and show the expected output if you can. It's helpful to have inline the smallest example of usage that you can demonstrate, while providing links to more sophisticated examples if they are too long to reasonably include in the README.
-
-## Support
-Tell people where they can go to for help. It can be any combination of an issue tracker, a chat room, an email address, etc.
-
-## Roadmap
-If you have ideas for releases in the future, it is a good idea to list them in the README.
-
-## Contributing
-State if you are open to contributions and what your requirements are for accepting them.
-
-For people who want to make changes to your project, it's helpful to have some documentation on how to get started. Perhaps there is a script that they should run or some environment variables that they need to set. Make these steps explicit. These instructions could also be useful to your future self.
+## Authors and acknowledgment
+Authors:<br> 
+<a href="mailto:antoniomattar132@gmail.com>">Antonio MATTAR</a>
+<a href="mailto:aiteldjouditamazouzt@gmail.com">Tamazouzt AIT ELJOUDI</a>
 
-You can also document commands to lint the code or run tests. These steps help to ensure high code quality and reduce the likelihood that the changes inadvertently break something. Having instructions for running tests is especially helpful if it requires external setup, such as starting a Selenium server for testing in a browser.
+Under the supervision of:<br>
+<a href="mailto:">Dr. Benjamin MONMEGE</a>
+<a href="mailto:">Julie PARREAUX</a>
 
-## Authors and acknowledgment
-Show your appreciation to those who have contributed to the project.
 
 ## License
-For open source projects, say how it is licensed.
-
-## Project status
-If you have run out of energy or time for your project, put a note at the top of the README saying that development has slowed down or stopped completely. Someone may choose to fork your project or volunteer to step in as a maintainer or owner, allowing your project to keep going. You can also make an explicit request for maintainers.
+GNU General Public License v3.0
+
+## Project status <a name = 'status'></a>
+The project development finished. However,
+If you want to contribute in this project, we did a small unfinished todo list:<br />
+TO DO LIST:<br>
+. Add a menu to choose the language of the program (English or French)<br />
+. Add a menu to choose the quality of images generated by the program.
+<font size='1'>(HIGH, MEDIUM, LOW)</font><br />
+.Add an option to save the reduction as an animation with alligators eating and sound effects.<br />
+.Add the possibility to deal with relative integers in the arithmetic operations.
+<font size ='1'> (NEED A GOOD KNOWLEDGE OF LAMBDA CALCULUS)</font><br />
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