On the subject of formations...

There are three 'main' formations which were made use of in this period. Of course, each of these formations was more of a 'category' than a general 'rule', which is to say that there was variation, both between nations and between commanders.

First, and most famous, was the line. Virtually every image of warfare from this period shows men standing in the line, typically three men deep, with bayonets fixed.
While the three-man deep line was quite common, it was, by no means, the ONLY depth used. The famous 'thin red line' at the Battle of Balaclava' was an example of a two-man deep line. Four-man deep lines were possible, but there were reports of casualties resulting from men being shot in the back by the rear rank. However, deeper lines than this were possible, where the rear ranks acted as a reserve and did not fire.
However, this negated two of the better points of the line formation. Firstly, it rendered the line vulnerable to cannon fire. In a 2-3 man deep line, a cannonball could only kill three men at most, or maybe wound six with a very lucky shot (discounting bouncing off of curved rocks, strong winds, and magic). The deeper the line, the more men a single cannonball can take out.
Secondly, and probably more importantly, a lines main advantage is that it allows more men to fire, giving you a greater 'surface area'.
The lines main disadvantage was poor mobility. It is VERY difficult to turn and maintain a line formation. Only veteran, well disciplined troops could turn in line without breaking formation. Lines were also slow, since marching in formation across anything other than a smooth, flat, surface is quite hard.

The column was favored by the Russians, mainly for the obvious reason that it gave both strong mobility and more 'punch' in bayonet combat, allowing more weight to be put on a single point. Since the Russian army favored the bayonet over the bullet (as noted in the previous Suvurov quotes), they generally sought to get into melee as soon as possible, allowing their artillery to do the 'softening up' in place of muskets.
The column formation has, as mentioned, two big advantages. Soldiers can move a lot faster in column, and maintain their formation as well. It also gives more weight to a charge.
The problems of columns come in the shape of cannons and muskets. Columns are not firepower-type formations, since only the first few ranks can fire. They are also very vulnerable to cannon fire, since a single cannonball, bouncing down the length of a column, can take out a whole row of soldiers.

The square is a typical defensive formation, best used to ward off cavalry. Often I hear it quoted that 'a square has only been broken by cavalry twice' or some other such nonsense. This is, of course, quite silly, but some have imbued the square with legendary cavalry-stopping abilities. While no doubt advantageous to the infantry in that it is impossible to flank a complete square, it is also essentially composed of four lines of infantry. Thus, if a charge takes place, it cannot be to the rear or flanks, which would probably lead to some casualties amoung the horses, but, in the end, a determined cavalry (with sufficient numbers) should be quite capable of destroying a square.
As mentioned, a square's advantage lies in its lack of flanks. All charges and attacks must be made to the 'front' of the formation.
However, a square is both totally immobile, and vulnerable to artillery, since artillery fire will pass through at least two lines of soldiers no matter the direction. Musket fire also presents an issue, since a square is typically even tighter than a line, and moving your men closer together makes them easier to hit.