Gradient flows of functionals on manifolds

Question

I'm reading some literature of ricci flows and on my way through it I quickly stumbled upon the gradien flow - one of the geometric flows. After searching on other books I found rigor definition of the gradient flow. However, in that book there was no further elaboration about it: like the properties, defining PDE origins, etc. Thus, I would really appreciate for a nice reference about the gradient flows (as a geometric flows on the manifolds).