This doesn't seem to be widely known (even though the nLab tells anyone who googles "quasi-category" or similar) but André Joyal's very nice and accessible pre-book/lecture notes (reference 44 in HTT) is available online
The pdf is here:
André Joyal, The theory of quasi-categories and its applications
This is bundled with lecture notes by Ieke Moerdijk on (oo,1)-operads and by Betrand Toën on derived stacks over simplicial rings in one remarkable collection of lecture notes, that was supposed to have been officially published already, but keeps being delayed:
Have a look. This is a very nice resource. But notice that these lecture notes were distributed before that course started and meanwhile improved and polished versions exist, likely available on request from the authors.