This book constitutes the proceedings of the 16th Latin American Symposium on Theoretical Informatics, LATIN 2042, which took place in Puerto Varas, Chile, in March 2024. The 44 papers presented in this volume were carefully reviewed and selected from 93 submissions. They were organized in topical sections as follows:Part I: Algorithms and Data Structures; Approximation and Online Algorithms; Complexity Theory; Part II: Combinatorics and Graph Theory; Parameterized Algorithms; Automata Theory and Formal Languages; and Game Theory and Fairness.