"Modular Forms with Integral and Half-Integral Weights" focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series. It is a fundamental problem to construct a basis of the orthogonal complement of the space of cusp forms; as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that the conclusion holds true for weight 3/2 by explicitly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. The book provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers and practitioners in modular forms of mathematics.

Theta Functions and Their Transformation Formulae.- Eisenstein Series.- The Modular Group and Its Subgroups.- Modular Forms with Integral Weight or Half-integral Weight.- Operators on the Space of Modular Forms.- New Forms and Old Forms.-Construction of Eisenstein Series.- Weil Representation and Shimura Lifting.- Trace Formula.- Integers Represented by Positive Definite Quadratic Forms.