  This thesis is devoted to the study of abelian automorphism groups of
surfaces and $3$-folds of general type over complex number field $\Bbb C$. We
obtain a linear bound in $K^3$ for abelian automorphism groups of $3$-folds of
general type whose canonical divisor $K$ is numerically effective, and we
improve on Xiao's results on abelian automorphism groups of minimal smooth
projective surfaces of general type. More precisely, the main results in this
thesis are the following. {\bf Theorem 3.0.} Let $X$ be a smooth 3-fold of
general type over the complex number field, $K$ the canonical divisor of $X$.
Let $G$ be an abelian group of automorphisms of $X$. Suppose $K$ is nef. Then
there exists a universal constant coefficient $c$ such that $\# G \le c K^3$.
