How to join only one row in joined table with postgres?

by 
select distinct on (author.id)
    book.id, author.id, author.name, book.title as last_book
from
    author
    inner join
    book on book.author_id = author.id
order by author.id, book.id desc

Check distinct on

SELECT DISTINCT ON ( expression [, …] ) keeps only the first row of each set of rows where the given expressions evaluate to equal. The DISTINCT ON expressions are interpreted using the same rules as for ORDER BY (see above). Note that the “first row” of each set is unpredictable unless ORDER BY is used to ensure that the desired row appears first.

With distinct on it is necessary to include the “distinct” columns in the order by. If that is not the order you want then you need to wrap the query and reorder

select 
    *
from (
    select distinct on (author.id)
        book.id, author.id, author.name, book.title as last_book
    from
        author
        inner join
        book on book.author_id = author.id
    order by author.id, book.id desc
) authors_with_first_book
order by authors_with_first_book.name

Another solution is to use a window function as in Lennart’s answer. And another very generic one is this

select 
    book.id, author.id, author.name, book.title as last_book
from
    book
    inner join
    (
        select author.id as author_id, max(book.id) as book_id
        from
            author
            inner join
            book on author.id = book.author_id
        group by author.id
    ) s
    on s.book_id = book.id
    inner join
    author on book.author_id = author.id

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