XPath select based on child value(s)

You can go with //book[./genres/genre = 'Romance'] and //book[./genres/genre = 'Romance' and ./genres/genre = 'Politics'], respectively

All books in Romance genre:

//book[genres/genre = 'Romance']

All books in Romance and Politics genre:

//book[genres/genre = 'Romance' and genres/genre = 'Politics']

All books in Romance that are also in Politics genre (same as and above):

//book[genres/genre = 'Romance'][genres/genre = 'Politics']

All books in Romance or Politics genre:

//book[genres/genre = 'Romance' or genres/genre = 'Politics']

All books in Romance or Politics genre (XPath 2.0 only):

//book[genres/genre = ('Romance', 'Politics')]

Notes:

//book finds all book elements anywhere beneath the root element; /books/book finds all book children of the books root element. For the given XML, they select the same elements.
You can append /author to any of the above XPaths to select the author elements of the books of the specified criteria.

Having trouble making it work?

First, establish that a basic XPath works: //book should return two elements.

If it does not:

Check spelling carefully of both the XPath expression and the XML.
Check case. XML and XPath are case sensitive.
Check that no namespaces are in play. Namespaces are effectively a part of the names of elements and attributes and must be accounted for. See How does XPath deal with XML namespaces?

Then, incrementally add XPath steps from there:

//book[genres] should select book elements with any genres child element.
//book[genres/genre] should select book elements with any genres child element, only if it in turn has a genre child element.
//book[genres/genre = 'Romance'] should select all books in Romance genre, as requested. Note that 'Romance' must be quoted; otherwise, the expression would be testing against the string value of a Romance child element of book and will certainly fail.