This course aims to give the basic concepts on the theory of Banach algebras. After the definitions followed by examples given in the first place, the second part of the course will deal with elements of spectral theory in Banach algebra. Then the case of commutative algebras will be closely examined, and finally, several examples of algebras of linear operators will be treated. The course is intended for those who take a first step in the theory of Banach algebra.