The primary objective of this course is to outline key guidelines for proving the classification of maximal connected algebraic subgroups of the Cremona group in dimension 3 over an algebraically closed field. The five lectures will address the following topics: - Lecture 1: Aims and scope\, a warm-up: tori and additive groups in the Cremona groups - Lecture 2: Standard conic bundles over rational surfaces - Lecture 3: Automorphism groups of standard conic bundles whose generic fiber is not P1 - Lecture 4: Mori del Pezzo fibrations of degree at most 6 over P1 - Lecture 5: Umemura quadric fibrations over P1