Source: gerbenbridge.blogspot.com.ar 
Read Conventions: Lebensohl-Rubensohl-Rumpelsohl
2NT has never been a popular contract, and rightly so. In many situations it does not pay to play 2NT as natural. Not because a hand that would want to bid it is not possible, but because there are better uses. Some examples are:
1NT (2) 2NT
(2) Double (Pass) 2NT
1 1 2 2NT
etc.
Conventions that end in “Sohl” use the transfer principle and use the extra 2NT step in these sequences as a transfer to 3 with several hand types. Let’s take the first sequence as example. Partner opens 1NT and RHO overcalls 2.
Lebensohl
2NT is a transfer to 3 with either a weak 1-suited hand below opponent’s suit (a minor) or some strong variations. With two bids, 3NT and 3, and by going through 2NT or not, you can distinguish about wanting to play 3NT with or without stopper in , and with or without 4-card . For suits above opponent’s () you have possible ways to show them.
Rubensohl
In this version by Ira Rubin all bids are transfers. The weak hands all bid the bid below the suit and then pass when partner completes the transfer. To ask only for a stopper for 3NT without 4-card major, transfer to 3NT with 3. Although the number of possible bids to show a suit is the same as Lebensohl, the number of sequences is larger because of more transfer bids. You can show a second suit, or show a suit and then ask for a stopper, for example.
Rumpelsohl
I’ve actually tried a third variation: Rumpelsohl. Here 2NT shows either a strong hand with or a weak hand with a suit below that of the opponents. The other bids are as in Rubensohl. These bids have the advantage that all bids except 2NT show a good hand.
Good things: You can also invite in suits lower than opponents except (opener will decline the transfer with a useful hand), and since you show a good hand, opener can get into to the auction when opponents raise. A big winner is this sequence: 1NT (2) 3.
Bad things: You lose the sequences where you show Clubs and were planning to bid a suit below opener’s after partner accepts. However partner is not barred from showing a big fit in the same way as after a Lebensohl 2NT. 1NT (2) 2NT (p) 3 = I can stand 4 if that is your suit!
Which should you play?
Although the number of sequences in Rumpelsohl (best imho) or Rubensohl is much richer and should be preferred in a regular partnership, the transfer nature of the bids make them more vulnerable for misunderstandings if you and your partner are not clear on which sequences to play the convention. This is why for casual partnerships I suggest you play Lebensohl.
Read Conventions: Lebensohl-Rubensohl-Rumpelsohl