Rotating an object around a fixed point using glMultMatrix

Since none of the previous answers look entirely correct and complete, let me try:

The key point to understand is that the transformations are applied to your vertices in reverse order of the order you specify them in. The last transformation you specify is the first one that is applied to your vertices.

This applies both to using calls like glTranslate and glRotate, and to using glMultMatrix. glTranslate and glRotate are convenience functions to build specific types of transformations, but they operate just like glMultMatrix.

In your example, to rotate around an arbitrary point, you need to first translate your vertices so that the rotation point moves to the origin, i.e. you want to translate by (-x, -y, 0). Then you apply the rotation. Then translate the origin back to the rotation point, which means a translation by (x, y, 0).

Now, since we need to specify these steps in reverse order, this means that your initial set of transformations is in the wrong order. It needs to be:

glTranslatef(x, y, 0);
glRotatef(theta, 0.0, 0.0, 1.0); 
glTranslatef(-x, -y, 0);

Your version using glMultMatrix looks correct, since you're already specifying the transformations in this order.

Assuming current matrix is ModelView Matrix, and the center of the object is at (x,y,0), the first sequence of translate, rotate, and then translate back seems correct sequence.

When using glMultMatrix instead, I don't think the sequence reverses but they are the same as the first sequence.

is sequence of matrices correct?!

The order of your first code snippet is correct, the second one though is not. The correct sequence is

glMultMatrix(Translation_Matrix);      // glTranslatef(x, y, 0);
glMultMatrix(Rotation_Matrix);         // glRotatef(theta, 0.0, 1.0, 0.0);
glMultMatrix(Neg_Translation_Matrix);  // glTranslatef(-x, -y, 0);

Keep in mind that glTranslate, glRotate and so on boil down to a function the makes a translation/rotation/... matrix and multiplies them using glMultMatrix.