I have been studying through the Reti Opening from the book Starting Out: The Reti.  I have enjoyed playing through positional masterpieces and learning the opening more completely.  I am concerned over the fact that Neil Mcdonald says the he tried to keep theory to a minimum in the book.  Is there theory, and long variations that are needed to be memorized, or can one easily get by in the Reti with a solid understanding of the resulting positions?  Thanks.

This is just one of the games from the book, I found it inspiring.

My understanding is that it is transpositional only if White plays a quick d4, or if Black find a way to transpose into the English with c5.  Are there other ways to transpose?

Could you be more specific?

I am confused.  Queen's Gambit, Queen's Indian, Grunfeld, and Catalans all need a d4 by White, do they not?

yes, for example :1.Nf3 d5 2. d4 nf6 3.c4 c6 4.Nc3 e6 and you get a semi slav or 1.Nf3 d5 2.c4 e6 3.d4 Nf6 QGD or 1.Nf3 c5 2.e4 going for sicialian lines.... the reti is a very transposional opening since the move Nf3 is used in many openings....Hope i helped...

You almost always play d4 at some time or another...(At least from my experience, which is not much.)

In the Reti d4 is often your primary pawn break to consider. Thus white may be destined to transpose into a queen's pawn game of some sort. 

The Reti is definitely not a good choice for beginners. Much of it's value comes from allowing experienced players to move order and avoid many of black's best defenses. Naturally, if you don't know what to avoid you don't know what to accept, and you'll largely be unable to find an advantage with the Reti since white is not staking his usual claim in the center. 

Interesting. My dad tried to learn me chess, when I was very young, by playing 1. Nf3 and also 1. e4 e5 2. Nf3 Nf6

Not a good opening repertoire, it seems....

Just to clarify:  By Reti I am referring to 1. Nf3 d5 2. c4, with the subsequent fianchetto of Bishop(s).