In this book, it is shown that the simple unital $C^*$-algebras arising as inductive limits of sequences of finite direct sums of matrix algebras over $C(X_i)$, where $X_i$ are arbitrary variable trees, are classified by K-theoretical and tracial data. This result generalizes the result of George Elliott of the case of $X_i = [0,1]$. The added generality is useful in the classification of more general inductive limit $C^*$-algebras.

Introduction 
Diagonalization, distinct spectrum and injectivity 
Berg technique 
Approximate divisibility 
Uniqueness theorem 
Existence theorem and classification

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