As far as I know Socrates is one of the first philosophers who started thinking about ethics and morals. So what book would you recommend me to read as a beginner in this topic. I recently read Early Greek Philosophy from Penguin publishing, maybe some similar book about Socrates and his views on ethics.
The Republic is pretty entertaining as a read, but as a source it doesn't summarize anything, obviously. Too, reading translations without context and understanding of the original intent, etc. can lead you to 'incorrect' beliefs about the meanings of words, terms, phrases or sentences as a result. But it's entertaining and pretty foundational.
This is just to update and review the answers after three years. You might try:
C.C.W. Taylor, Socrates: A Very Short Introduction. ISBN 10: 0198835981 / ISBN 13: 9780198835981 Published by Oxford University Press, United Kingdom, 2019.
Peter Adamson, Classical Philosophy: A history of philosophy without any gaps, Volume 1. ISBN 10: 019876703X / ISBN 13: 9780198767039 Published by Oxford University Press, 2016.
Adamson gives a sound account of Socrates' thought, so far as it is known, and leads on to Plato and Aristotle.
An older book, not mentioned so far but well worth reading, is:
J. Ferguson, Socrates: A Source Book. ISBN 10: 0333117034 / ISBN 13: 9780333117033 Published by Macmillan, 1970.