opening 1.c4-e5 2.Nc3-Bb4 3.Nd5-Bd4

hello. I have been studying the English opening as white.

If White plays Bc5 in response to  ND5. then it doesen't make sense to me to go with 4.d4-    Please can you share how would you play this opening,and what your intentions are. if you are white :

1.c4-e5 2.Nc3-Bb4 3.Nd5-Bc5

I possibly would play b4, as the bishop must retreat

After 4...Bf8 5 Bb2 C6 6Ne3 and you have a space advantage

I've only met it the once (against a Russian FM) in almost 100 games with the English. It is a very popular line at the GM level but, surprisingly, not at our level. Shirov has played it a few times with black so you should be able to find a lot of material online or in databases/books with it.

I played 4. e3 in my game, gaining an advantage, but that wasn't due to the opening.

Mihail Marin has written a trilogy repertoire book for Quality Chess on the English. He suggests the move order 1. c4 and 2. g3 against everything (except 1...b6 of course!).

ps. I am sure you meant 3...Bc5. Black has also tried 3...Ba5 and, most popular by far, 3...Be7