This book offers something new, every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes, (i) the correspondence between the forms of half-integral weight and those of integral weight and (ii) the arithmeticity of various Dirichlet series associated with modular forms of integral or half-integral weight.