Abstract: This chapter presents five interesting categories of solutions that will play a role in the development of the theory of the book: separate-variables solutions, traveling waves, source-type solutions, blow-up solutions, and constant-height solutions. Other solutions, such as dipoles and general fronts, will be used to complete the picture. Important concepts for the sequel are introduced, such as scaling, limit solutions, finite propagation, free boundaries, existence under optimal conditions, blow-up, limited regularity, and initial traces.

Keywords: separate-variable solutions, traveling waves, source-type solutions, blow-up solutions, constant-height solutions, dipoles, general fronts,