user9148: Queen, in a sense, is equivalent to Bishop and Rook. What is the logic behind "putting Rook and Bishop" in the promotion move's options? Why doesn't it (Promotion move) provide the choice between Queen and Knight only? Why would one promote his Pawn to Rook or Bishop other than Queen? Promoting to Rook/Bishop instead of Queen may provide smaller advantage than promoting to Queen, and it may even provide a disadvantage to the mover. 

user3529: There are situations where promotion to a knight leads to draw and promotion to a queen leads to stalemate.  In these cases rook or bishop may be necessary to cash in the full point.

user9030: There are 3 types of piece moves in chess:

Straight
Diagonal
Knight-move

There are positions, where promoted piece takes away the last square that enemy king can move, and stalemates. This happens because of one of these move types.
To avoid stalemate and win eventually, you have to select a promotion which doesn't have stalemating move, which is called underpromotion.
For example, if diagonal move stalemates, you can't select queen as it has diagonal move ability. But you can select a rook, and go for a win.
Example from famous Saavedra position:
[FEN "8/8/1KP5/3r4/8/8/8/k7 w - - 1 1"]
[Title "Saavedra"]    

1. c7 Rd6+ 2. Kb5 Rd5+ 3. Kb4 Rd4+ 4. Kb3 Rd3+ 5. Kc2 Rd4 6. c8=Q ( 6. c8=R Rc4+

7. Rxc4 Ka2 8. Ra4# ) (6.Kc3 Rd1 7. Kc2 Rd4) Rc4+ 7. Qxc4=/=


user924: Sometimes, choosing a bishop or a rook is the best move, because of stalemate possibilities. This happens most often with rooks, and very rarely with bishops.
For instance, in this famous position from the Saavedra problem:
[FEN "8/2P5/8/8/3r4/8/2K5/k7 w - - 0 1"]

If white plays 1.c8Q, then black plays 1...Rc4+. White needs to take it or lose his queen but after 2.Qxc4 it is stalemate.
If instead white plays 1.c8R, the stalemate trick doesn't work and 2.Ra8+ with checkmate next move is threatened. So black must play 2...Ra4, but white plays 3.Kb3 attacking the rook and also threatening 4.Rc1 checkmate; black can't deal with both threats.
On Tim Krabbe's page on practical minor promotions I found this example from Kholmov-Ehlvest 1983:
[FEN "2k5/2P5/1K2p3/7r/8/8/7p/R7 b - - 0 1"]
[StartFlipped "0"]

(black to move)
White threatens to play Ra8+ and c8Q+. If black promotes to a queen with 1...h1Q, then that isn't enough for black to win: 2.Ra8+ Qxa8 is stalemate.
Promoting to a rook or knight clearly doesn't help black.
But after 1...h1B, the check doesn't work, black is simply a piece up and has a winning position.

9148: <p>Queen, in a sense, is equivalent to Bishop and Rook. What is the logic behind "putting Rook and Bishop" in the promotion move's options? Why doesn't it (Promotion move) provide the choice between Queen and Knight only? Why would one promote his Pawn to Rook or Bishop other than Queen? Promoting to Rook/Bishop instead of Queen may provide smaller advantage than promoting to Queen, and it may even provide a disadvantage to the mover. </p>
 3529: <p>There are situations where promotion to a knight leads to draw and promotion to a queen leads to stalemate.  In these cases rook or bishop may be necessary to cash in the full point.</p>
 9030: <p>There are 3 types of piece moves in chess:</p>

<ol>
<li>Straight</li>
<li>Diagonal</li>
<li>Knight-move</li>
</ol>

<p>There are positions, where promoted piece takes away the last square that enemy king can move, and stalemates. This happens because of one of these move types.</p>

<p>To avoid stalemate and win eventually, you have to select a promotion which doesn't have stalemating move, which is called underpromotion.</p>

<p>For example, if diagonal move stalemates, you can't select queen as it has diagonal move ability. But you can select a rook, and go for a win.</p>

<p>Example from famous Saavedra position:</p>

<pre><code>[FEN "8/8/1KP5/3r4/8/8/8/k7 w - - 1 1"]
[Title "Saavedra"]    

1. c7 Rd6+ 2. Kb5 Rd5+ 3. Kb4 Rd4+ 4. Kb3 Rd3+ 5. Kc2 Rd4 6. c8=Q ( 6. c8=R Rc4+

7. Rxc4 Ka2 8. Ra4# ) (6.Kc3 Rd1 7. Kc2 Rd4) Rc4+ 7. Qxc4=/=
</code></pre>
 924: <p>Sometimes, choosing a bishop or a rook is the best move, because of stalemate possibilities. This happens most often with rooks, and very rarely with bishops.</p>

<p>For instance, in this famous position from the Saavedra problem:</p>

<pre><code>[FEN "8/2P5/8/8/3r4/8/2K5/k7 w - - 0 1"]
</code></pre>

<p>If white plays <strong>1.c8Q</strong>, then black plays <strong>1...Rc4+</strong>. White needs to take it or lose his queen but after <strong>2.Qxc4</strong> it is stalemate.</p>

<p>If instead white plays <strong>1.c8R</strong>, the stalemate trick doesn't work and 2.Ra8+ with checkmate next move is threatened. So black must play <strong>2...Ra4</strong>, but white plays <strong>3.Kb3</strong> attacking the rook and also threatening 4.Rc1 checkmate; black can't deal with both threats.</p>

<p>On <a href="http://timkr.home.xs4all.nl/chess2/minor.htm" rel="noreferrer">Tim Krabbe's page on practical minor promotions</a> I found this example from Kholmov-Ehlvest 1983:</p>

<pre><code>[FEN "2k5/2P5/1K2p3/7r/8/8/7p/R7 b - - 0 1"]
[StartFlipped "0"]
</code></pre>

<p>(black to move)</p>

<p>White threatens to play Ra8+ and c8Q+. If black promotes to a queen with <strong>1...h1Q</strong>, then that isn't enough for black to win: 2.Ra8+ Qxa8 is stalemate.
Promoting to a rook or knight clearly doesn't help black.</p>

<p>But after <strong>1...h1B</strong>, the check doesn't work, black is simply a piece up and has a winning position.</p>
