At least 3 Madison bridge players have asked me to write out Bergen raises. Here is a summary, but I strongly recommend the original source. "Better Bidding with Bergen," by Marty Bergen, Volume I, published in 1985. This summary by Stan Fuhrmann.

This article is not intended to be a substitute for reading Marty Bergen's discussion of these bids. But, many bridge players in Madison use some variation of the following, and you will be better off knowing what the bids mean, even if you choose to not use this bidding structure

In all examples, assume that partner has opened 1  or 1 , and that second hand has passed.

Bergen Raises as used by many, but not all, in Madison

Response to 1 of Major opening	Bergen approach	Bergen Raises As played in Madison
1N		Many in Madison play this as forcing, even if a passed hand. The 1N bidder typically has one of 4 hand types. (a) around 6-10 hcp with 2 trump, intending to return to 2 of the major (b) balanced invitational (or maximum if passed hand) with at most 2 trump, intending to rebid 2N (c) limit raise with exactly 3 trump, intending to rebid 3 of major (d) misfit, hoping to find a better spot (could be very weak)
raise to 2 of major	3 card support, about 5-9 hcp	same as original Bergen.
2 NT	Jacoby 2N (game force with 4+ card support)	Most use the 2N as an artificial game force, but not necessarily the Jacoby 2N
3	4-card constructive raise; about 7+ to a bad 10	See the 3 response. Most here, and also in other parts of the country, have reversed the meanings of the 3  and 3  bids. The principle is: The better the hand, the lower the bid. The 3  bid gives partner at least 1 bid below 3 of the major to make a game/slam try bid (which forces responder to bid again). So, in Madison, 3  is usually the LIMIT raise
3	4-card limit raise; about a good 10+ to a so-so 12	See above. In Madison, 3  is the constructive raise. Here is an example of how responder can use this bid and still reach game even if partner signs off at the 3-level: Partner opens 1 , and you have Kxxx Axxx x xxxx. You have only 7 hcp, but every honor card is working, and you have a stiff. First bid 3 , and then raise to game if partner signs off in 3 . This bid shows some defensive values, and is better than an immediate jump to game. If opponents compete, partner will know what to do.
3 of major	4-card preemptive raise, 0-6 hcp	Same as Bergen, except that different partnerships may have slightly different agreements about the definition of a preemptive raise.
Jump to 3 of OTHER major	Splinter bid, with relays. Example: After a jump to 3 , (spades are trump) 3  now asks for the shortness. 3N response(first step)=Club stiff, 4 (second step)=Diamond stiff, 4 (third step)=stiff in other major (hearts in this case)	At least 2 Madison partnerships play this or something similar. One Madison partnership plays that a JUMP SHIFT in the other major is a splinter. However, most partnerships that use Bergen raises in Madison do not use this. For them, a jump shift is a natural bid.
3N	3-card balanced non-forcing raise	Madison is all over the map here. Some play that the jump to 3N promises exactly 2-card support. Others play it is either 2 or 3-card support, but a balanced hand in the 12+ to 15 range. One pair has agreed that it shows exactly 3, headed by AT BEST the Jack. So, YOU DECIDE.
4	BIG balanced raise, good 3-card support, too good for 3N. This can be described as a Value Swiss Raise with 3-trump	A few in Madison play it this way. The cutoff for HCP is usually 16+. At least one partnership has agreed that this bid promises at least one of the top 3 honors. However, most in Madison that play Bergen raises have not redefined the 4 of a minor bids, so this bid is still an ordinary splinter in support of opener's major.
4	GOOD raise to 4; say 5-card support and around 8-10 hcp	As far as I know, no one in Madison plays it this way. Most play that this is a splinter in diamonds (same as for clubs). If 4 (above) is 16+ with good 3-card support, then some play that this is around 13-15, with good 3-card support. One partnership has agreed that this bid promises at least one of the top 3 honors. To show the hand that Bergen suggests, most that use Bergen will bid 3 , and then raise to game if partner signs off at the 3-level. However, most play that this is a splinter in diamonds (4  above is a splinter in clubs)
4 of OTHER major	natural and preemptive	If playing the usual splinter complex, 4 over 1  is a splinter in hearts. If you play the other style for splinters, 4  over 1  is to play. AND I and EVERYONE suggest that you know which is which! If you bid 4  over partner's 1 , you deserve any bad result that you get.
immediate raise to game	natural, WEAK, and preemptive	Same as Bergen. If you have defensive values (say 8-10 hcp) and 5 trump, you should first bid 3 , and then raise to game.