TITLE: Introductory texts on manifolds
QUESTION [66 upvotes]: 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.

REPLY [3 votes]: I'm way late to the party, but for an example requiring very very few prerequisites, Reyer Sjamaar's notes on Manifolds and Differential Forms are very well-organized and accessible.  They can be accessed for free here on his website.  Perhaps too elementary, but I'm not entirely sure of your background.