The paper is an account on the birth of one of the fundamental mathematical disciplines that evolved in the 20th century, i.e. functional analysis. It focuses on the contributions of the Polish mathematicians in the period between the two World Wars, in particular those that appeared in the first volumes of the journal “Studia Mathematica", that was edited by S. Banach and H. Steinhaus and was “one of the first journals in the history that was specialized only in some areas of mathematics". The most classical theorems of functional analysis were published in this journal, and are described in this paper. A special section is devoted to Banach, his life and the importance of his contributions to mathematics, including many interesting facts, like the story about the Scottish Café in Lvov. The paper ends with a (46 items) long list of references of interest for the history of functional analysis, and is altogether a very interesting and easily readable introduction into this field that could be of interest not only to mathematicians working in the field or in history of mathematics, but also to others interested in the ideas and persons who formed functional analysis.