Having said that here are some suggestions for introductory reading. Some of the problems of the following 1992 collection have, naturally, been solved.

B. Bielefeld and M. Lyubich (eds): Problems in Holomorphic Dynamics. 1992.

The following two papers are concerned with quadratic polynomials.

D. Schleicher: Rational Parameter Rays of the Mandelbrot set. 1997

The following two papers are concerned with polynomials of any degree.

J. Milnor (appendix A. Poirier): Hyperbolic components in spaces of polynomial maps. 1992.

J. Kiwi: Rational Rays and critical portraits of critical polynomials.

J. Milnor: On rational maps with only two bicritical points.

Finally, here are two papers concerned with the family of exponential maps.

D. Schleicher and J. Zimmer: Dynamic rays for exponential maps.

L. Rempe and D. Schleicher: Bifurcations in the space of Exponential Maps