A typical gap theorem of the type discussed in the book deals with a set of exponential functions on an interval of the real line and explores the conditions under which this set generates the entire space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various properties of zeros of analytic functions in one variable.