I am looking for a harmony text book introducing the fundamental conventions of four part writing as well as uses of common chords and progressions. I want to be able to work through it myself over the summer so it needs to be easy to understand and follow with good explanations and exercises. Any suggestions?

For your case, I would strongly suggest picking up "Harmony and Voice Leading" by Edward Aldwell and Carl Schachter (get the 3rd edition, if possible). This is the theory book I've been working out of for the past few months and it's going great. It has some great exercises at the end of each chapter and great examples throughout. The explanations are quite good but I will tell you that sometimes you may have to read a particular paragraph over a couple times to actually get it. Essentially if you read it from the beginning (square one, so to speak) there would be no reason as to why you would not be able to understand the later stuff. It gets quite complex, but you should only assume that out of any respectable harmony textbook. It also has your four part writing covered as there is a whole unit talking about that, common chords and progressions are just naturally introduced as you study the book as there is a strong emphasis on developing a good tonal languange.

If and when you master this book, I would suggest you check out Arnold Schoenberg's "Structural Functions of Harmony". It's what I refer to as the 'next step up' and provides great new ways of looking at how harmony actually works and great insight into the music of the Romantic era focusing on complex voice leading to help you write music like the great Romantic era composers.

Hope this will provide a solid starting ground!