What is a good introduction in gradient flows in metric spaces? I know the book Gradient flows: in metric spaces and in the space of probability measures by Luigi Ambrosio, Nicola Gigli and Giuseppe Savaré, but is too hard for an introduction.
Can someone make this a community wiki? I cannot find how you have to do that...
To close this question I will post the answer which I got at Mathoverflow.
I have read Philippe Clément's notes on gradient flows in metric spaces.
Another nice book which I have found is the book "Optimal Transport, old and new" by Cédric Villani". Nice book. It is in the Yellow Sale in Europe until the end of July.