The Fundamentals of Analyses: How I Started to be a Researcher is a basic course I modified for the beginners who wish to start doing research and mathematical journal. In fact, this is how I started to study in order to create papers. The content of this book shows basic steps and foundations on making mathematical arguments, writing a very good mathematical statements as introductions of making claims and conjectures, shows on how to write basic proofs and provides well-known theorems and claims that would help us to start our own research.