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Over the past few decades, orthogonality in special spaces has been developed into an important eld of study in mathematics. The main purpose of this book is to present many of the results and generalizations of this concept. Of course, not all aspects of this concept could be included in this exposition. The book contains four chapters. The rst chapter is devoted to some of the basic results of nonlinear functional analysis. In Chapter 2, we consider orthogonality in normed spaces and operator norm attainment in inner product spaces. This includes the most recent work in the literature. We answer to this question, whether a linear map which approximately preserves orthogonality must be close to an orthogonality preserving one in chapter 3. Our treatment of the main subject in the book are in Chapter 4. In this chapter, we give new generalizations of the orthogonality concept.