The book is mainly aimed at the bilingual curriculum design of discrete mathematics.It can meet the needs of the types of an introduction to the fundamental ideas of discrete mathematics,and as a foundation for the development of more advanced mathematical concepts.The book includes four parts.The first part is mathematical logic which covers propositional logic in Chapter 1 and predicate logic in Chapter 2.It gives a method how to express natural language statements using symbols as the foundation to discrete mathematics,especially for sets.The logic parts include equivalent calculation and the discussion of proof.The second part is set theory with sets in Chapter 3,relations in Chapter 4,and functions in Chapter 5,which is the basics of the whole mathematics.Chapter 3 presents basic types of sets and their operations.Chapter 4 presents definition,properties and operations of relations,along with their representation as directed graphs and connections with matrices.Chapter 5 restates the function from the perspective of relations,including countable sets and uncountable sets.The third part is graph theory in Chapter 6 which is the sources for data structures and algorithms.It covers terminology,representation and special structure of graphs.The last part,that is a highly abstract part,is algebraic systems in Chapter 7,which covers semigroups,groups rings and fields.By algebraic systems we can find commonalities of many familiar rules.This book can be used as a discrete mathematics courses reference for computer,mathematics,big data technology and some related disciplines in Institutions of Higher Learning,and can also provide useful help for other readers of discrete mathematics,especially for bilingual learning.