A formal group is an algebraic analogue of a Lie group. Lie groups are any smooth, chartable objects, such as circles, globes or lines, that contain points which obey group properties and that have differentiable group operations.
Group properties include the algebraic properties of the associative property, the identity property and the reciprocal property in addition to closure. Closure simply means that there is no operation a person can perform using the elements of the group that would produce a sum, product, dividend or other result that is outside the group. Formal groups satisfy all the constraints put on Lie groups, but they are expressed algebraically, in terms of numbers and equations, rather than geometrically, as points on a figure.