How to use Lie Groups in differential equation

Hi all. I remember somebody saying in this news group that Lie Groups 
(symmetry analysis) was a general purpose approach to solving 
differential equations. I've been googling the web for a week now in 
order to understand how this works, and now have a bit of an 
understanding of what an algebra/group is (and specifically what Lie 
algebras and groups are).

However, each time I try to understand how Lie algebra applies to 
differential equations, I slam into a wall of mathematical symbolism.

My mathematics training is 1 1/2 years university level as part of a 
bachelor of science, and then self-trained. I'm up to date on 
differentiation, calculus, vectors, matrices, complex numbers and 
quaternions, but I've had very little training in mathematical symbolism.

So, does anyone have any links to free resources that covers this topic 
at a 2nd/3rd year university level? Preferably with some worked examples? :)

Thank you,

Joal Heagney