I have been told by different people that probably no subject can unify algebra, analysis and geometry better than Riemann surfaces. Regardless of how true it is, I'm looking for a textbook that explains the basic ideas and theorems of Riemann surfaces with a fairly reasonable background which includes undergraduate algebra, undergraduate analysis and undergraduate geometry.
In other words, the audience of the book should be advanced undergrad students. Since I want it for self-study, I'd really like to find a book that has solutions. If not, then a textbook with graphics, drawings or intuitive explanations would suit me the best.
I'm tagging this question as 'reference-request' and 'soft-question'. I will really appreciate it if you share with me your pedagogical experience or your own troubles when you wanted to get introduced to Riemann surfaces. Any piece of advice about how to approach the subject is welcome and highly appreciated