In this monograph, we study complexity classes that are defined using $O(\log n)$-space bounded non-deterministic Turing machines. We prove salient results of Computational Complexity in this topic such as the Immerman-Szelepcs$\rm\acute{e}$nyi Theorem, the Isolating Lemma, theorems of Mahajan-Vinay on the determinant and many consequences of these very important results. The manuscript is intended to be a comprehensive textbook on the topic of The Complexity of Logarithmic Space Bounded Counting Classes.

翻译：在本专著中，我们研究由$O(\log n)$空间有界非确定性图灵机定义的复杂性类。我们证明了该领域中计算复杂性的一些重要结果，例如Immerman-Szelepcs$\rm\acute{e}$nyi定理、隔离引理、Mahajan-Vinay关于行列式的定理，以及这些重要结论的诸多推论。本手稿旨在成为关于"对数空间有界计数类的复杂性"这一主题的综合性教科书。