The article represents an excellent exposition of a fascinating, resurgent field of research, by one of the main researchers in the domain. It starts from the basic physical intuition and motivation, proceeds through essential background material, such as the mean curvature flow, as well as crucial definitions and tools from geometric measure theory, of which the notion of varifold is the key one, and attains the detailed presentation and comprehensive proof of a new existence theorem as well as regularity theorems, and also the exploration of singularities formation. The text thus represents a lucid and alluring, compact yet at the same time detailed introduction to the Brakke flow, that will provide an excellent source for future researchers in the field and those interested in its applications.