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

I have the following schema:

CREATE TABLE author (
    id   integer
  , name varchar(255)
);
CREATE TABLE book (
    id        integer
  , author_id integer
  , title     varchar(255)
  , rating    integer
);

And I want each author with its last book:

SELECT book.id, author.id, author.name, book.title as last_book
FROM author
JOIN book book ON book.author_id = author.id

GROUP BY author.id
ORDER BY book.id ASC

Apparently you can do that in mysql: Join two tables in MySQL, returning just one row from the second table.

But postgres gives this error:

ERROR: column "book.id" must appear in the GROUP BY clause or be used in an aggregate function: SELECT book.id, author.id, author.name, book.title as last_book FROM author JOIN book book ON book.author_id = author.id GROUP BY author.id ORDER BY book.id ASC

It's because:

When GROUP BY is present, it is not valid for the SELECT list expressions to refer to ungrouped columns except within aggregate functions, since there would be more than one possible value to return for an ungrouped column.

How can I specify to postgres: "Give me only the last row, when ordered by joined_table.id, in the joined table ?"

Edit: With this data:

INSERT INTO author (id, name) VALUES
  (1, 'Bob')
, (2, 'David')
, (3, 'John');

INSERT INTO book (id, author_id, title, rating) VALUES
  (1, 1, '1st book from bob', 5)
, (2, 1, '2nd book from bob', 6)
, (3, 1, '3rd book from bob', 7)
, (4, 2, '1st book from David', 6)
, (5, 2, '2nd book from David', 6);

I should see:

book_id author_id name    last_book
3       1         "Bob"   "3rd book from bob"
5       2         "David" "2nd book from David"

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

I've done something similar for a chat system, where room holds the metadata and list contains the messages. I ended up using the Postgresql LATERAL JOIN which worked like a charm.

SELECT MR.id AS room_id, MR.created_at AS room_created, 
    lastmess.content as lastmessage_content, lastmess.datetime as lastmessage_when
FROM message.room MR
    LEFT JOIN LATERAL (
        SELECT content, datetime
        FROM message.list
        WHERE room_id = MR.id
        ORDER BY datetime DESC 
        LIMIT 1) lastmess ON true
ORDER BY lastmessage_when DESC NULLS LAST, MR.created_at DESC

For more info see https://heap.io/blog/engineering/postgresqls-powerful-new-join-type-lateral

This may look archaic and overly simple, but it does not depend on window functions, CTE's and aggregating subqueries. In most cases it is also the fastest.

SELECT bk.id, au.id, au.name, bk.title as last_book
FROM author au
JOIN book bk ON bk.author_id = au.id
WHERE NOT EXISTS (
    SELECT *
    FROM book nx
    WHERE nx.author_id = bk.author_id
    AND nx.book_id > bk.book_id
    )
ORDER BY book.id ASC
    ;

Here is one way:

SELECT book_id, author_id, author_name, last_book
FROM (
    SELECT b.id as book_id
         , a.id as author_id
         , a.name as author_name
         , b.title as last_book
         , row_number() over (partition by a.id
                              order by b.id desc) as rn
    FROM author a
    JOIN book b 
        ON b.author_id = a.id
) last_books
WHERE rn = 1;