Reference book for Galois Representations

Galois representations have to come from somewhere.

If you are not interested in learning about modular forms and automorphic forms at this point, the other best source of representations are elliptic curves. You can find a gentle introduction in Silverman's book "The Arithmetic of Elliptic Curves", particularly the chapter on Tate modules.

As an alternative, for a completely "algebraic number-theoretic" approach, you might want to learn about complex Galois representations and their Artin L-functions. This is covered for example of Neukirch's book on ANT [Chapter VII] or Lang's [Chapters VIII and XII]. There's a lot of interesting and accesible number theory around it. That said, this alone won't get you too far in the way of understanding the big picture of Galois representations.

A nice general overview which doesn't jump directly into automorphicity issues is Richard Taylor's survey "Galois Representations", but it gets technical very quick.

You also might want to keep in mind the more advanced references in Emerton's great answer to this question.

There's also plenty of introductory text to modular forms. "A First Course in Modular Forms" has alredy been mentioned in the comments. The classic "A Course in Arithmetic" by Serre is probably the best general textbook on number theory that covers the basic of modular forms.

You can see the book of J.P.Serre "Abelian l-adic representations and elliptic curves" a very nice presentation of Galois representations and properties !