The paper summarizes the contributions and the discussions to the INDRUM Working Group on Research on Number Theory, Algebra, Discrete Mathematics, Logic. Ten oral communications have been presented, reflecting the variety of the thematic of Number Theory, Algebra, Discrete Mathematics, Logic. 2 papers on Linear Algebra (Span, Linear transformation); 2 papers on Abstract Algebra (Group theory, concept of Ideal); 4 papers on logic, reasoning and proof (Syntax and semantic, Mathematical induction and recursion, Backward reasoning, Personal meaning of proof); 2 papers on innovative teaching (First year university students, Geometry capstone course).