I am looking for a comprehensive book on Probability which discusses Convergence of Random Variables in detail, excluding portions of Measure Theory. Allan Gut's "Probability: A Graduate Course" seems fabulous, but it has way too much content on Measure Theory, which I do not know at all.

There is a wealth of professors and undergrad students of Stats and Maths on this website; and I would like to directly ask you: which book should suit my situation? Because I CAN learn Measure Theory but considering I am only a first year undergrad, and Measure Theory will be taught to me three years later, I suppose it will only be a wastage of time.

incredibly cool. See it now so you can see more later! $\endgroup$ – Noah Schweber Jan 23 '15 at 18:13