Irving Copi's Introduction to Logic discusses analogies in depth and yet at an undergraduate level.
Since this book presents logic in general it also has parts on other topics related to logic such as informal arguments, language and deduction. Even the section on analogies is part of a larger presentation on induction which includes causal connection, science and probability. One can view these other topics as context to help one better understand analogy.
Copi notes that arguments by analogy are common: (page 389)
Not all arguments are deductive, however. A great many arguments are not designed to demonstrate the truth of their conclusions as following necessarily from their premisses, but are intended merely to support their conclusions as probable, or probably true.
He presents the form of an analogical argument: (page 392)
a,b,c,d all have the attributes P and Q.
a,b,c all have the attribute R.
Therefore, d probably has the attribute R.
An analogical argument is not valid like a deductive argument, but some can be described as weaker than others. Copi provides six criteria for helping one to decide when an argument from analogy is weak or strong.
Although the section explicitly on analogies is short, they provide a ground for induction which covers a third of the book. The other parts of the book provide contrast and context for where analogy fits in the study of logic.
Copi. I. M. Introduction to Logic. Sixth Edition. Macmillan (1982)