As a new-comer to the topic of manifolds, learning it from math textbooks is painful. That seems to be the case even if you're reasonably strong at analysis, to

As a new-comer to the topic of manifolds, learning it from math textbooks is painful. That seems to be the case even if you're reasonably strong at analysis, topology and linear algebra. I find textbooks written for theoretical physicists much gentler read. Physics textbooks can be a good place to start learning, say, differential geometry even if you don't care about physics (I don't).