I was studying some hyperbolic geometry previously and realised that I needed to understand things in a more general setting in terms of a "manifold" which I don't yet know of.

I was wondering if someone can recommend to me some introductory texts on manifolds, suitable for those that have some background on analysis and several variable calculus. A lecturer recommended to me "Analysis on Real and Complex Manifolds" by R. Narasimhan, but it is too advanced.

I had a look at Loring W. Tu's text on manifolds and it seemed accessible.