This book constitutes the proceedings of the 18th International Colloquium on Theoretical Aspects of Computing, ICTAC 2021, organized by the Nazarbayev University, Nur-Sultan, Kazakhstan. The event was supposed to take place in Nur-Sultan, Kazakhstan, but due to COVID-19 pandemic is was held virtually.The 15 papers presented in this volume were carefully reviewed and selected from 40 submissions. The book also contains one invited talk in full paper length. The book deals with challenges in both theoretical aspects of computing and the exploitation of theory through methods and tools for system development.The 20 full papers presented in this volume were carefully reviewed and selected from 55 submissions. The papers cover a wide variety of topics, including: getting the best price for selling your personal data; attacking Bitcoin; optimizing various forms of model checking; synthesizing and learning algorithms; formalizing and verifying contracts, languages,and compilers; analyzing the correctness and complexity of programs and distributed systems; and finding connections from proofs in propositional logic to quantum programming languages.