Abstract
This text is the result of a course given at the Centre international de rencontres mathématiques in Luminy from 26 to 30 may 2003. In the first chapter, we introduce the theory of modular forms with integral weight on Γ0(N). The second chapter is devoted to the study of periods of modular forms on Γ0(1) and the integral structures implied by these periods. In the third chapter the notions of quasi modular forms and quasi holomorphic modular forms on Γ0(1) are introduced as well as the links with differential operators. At least, the notion of half integral modular forms with multiplicative system is presented in an annex.