I'd defer to /u/mathbbR's recommendations. For your convenience, I'll include Amazon links to those three titles:

• Fractals: A Very Short Introduction by Kenneth Falconer.

• Fractals Everywhere by Michael F. Barnsley.

• Fractal Geometry: Mathematical Foundations and Applications by Kenneth Falconer.

I'd add the following suggestion:

• Measure, Topology, and Fractal Geometry by Gerald Edgar.

Good luck in your studies!