は vs が? (as particles)

[ethanfone]

Can anyone help me with the difference between が and は? I'm pretty confused, and I'm having trouble telling which one of these is correct:

あの犬は私のです。 or　 あの犬が私のです。

Thanks in advance!

[LeonVP.]

if bad I don't remember, は is used as a topic particle, so it's used if the theme is the same as before, while が is used to mark the subject, as if you we're changing the themes, both means the same but have different usages (forgive my English).

[BJCUAl]

This has been covered before and there are multiple online resources for this question.

あの犬は私のです　That is my dog. (simple statement)

あの犬が私のです　That is my dog. (specifying which dog out of many)