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LTSpice is a free circuit simulation program from Linear Technology.
The circuit consists of nodes with component elements connecting them.
The idea is that Spice can solve a set of simultaneous equations using the component values in a matrix. You can find "The Spice Book" on the web which gives a run down on how Spice works. LTSpice has a schematic editor for entering the circuit. You can do transient analysis or ac analysis and a number of other analysis's.
After you have run the simulation you can put the mouse on a node to see the voltage wave for or over the lead of a component to see the current wave form. LTSpice comes with a library of components but you can specify your own component models or use pspice3 models from the web. LTSpice is designed for windows but will work on the wine windows emulator under Linux.

Another useful program is Scilab from Inria in France.
The website is something like scilab.org. Sorry Mike, I've forgotten the format of the a href html tag. Scilab can be used to calculate simple lumped component circuirs such as filters and so on. Scilab is a sort of poorman's Matlab. There are versions of Scilab for Windows as well as Linux. There is Octave for Linux but I found Scilab more comprehensive. There are also a number of toolboxes for things like image processing and so on for Scilab.