Setup the tables and some sample data:

drop table if exists users;
drop table if exists views;
drop table if exists tracks;

create table users
(idu      int
,username varchar(30));

create table views
(id       int
,`by`     int
,track    int);

create table tracks
(id       int
,uid      int
,title    varchar(30)
,time     datetime);

insert into users values
(567,'TrainingPuppy'),
(687,'BathroomMakeover'),
( 45,'PoshNachos'),
( 15,'SewingButtons');

insert into views values
(1,  5, 55),
(2,  5, 55),
(3, 67, 55),
(4,  6, 29),
(5,125,  2),
(6,  5,698),
(7,  5,698);

insert into tracks values
(  2, 15,'Worf is in the air','2016-02-11 22:57:35'),
( 29,567,'Stargold'          ,'2016-08-11 22:57:28'),
( 55,567,'No love liers'     ,'2016-10-11 22:57:51'),
(698,567,'Lofe'              ,'2016-11-11 22:57:44');

Start with a (ANSI standard group by) query to obtain our counts:

select tracks.id,
       tracks.uid,
       count(*) as ucount,
       users.username,
       views.track,
       tracks.title,
       tracks.time

from   tracks
join   views
on     views.track = tracks.id

join   users
on     users.idu = tracks.uid

group by tracks.id,
         tracks.uid,
         users.username,
         views.track,
         tracks.title,
         tracks.time

We'll call the above 'user_counts', and create a query that generates a ranking over username ordered by ucount desc:

select id,
       uid,
       ucount,
       username,
       track,
       title,
       time,
       @user_rank := if(@current_username = username, @user_rank:=@user_rank+1, 1) as user_rank,
       @current_username := username

from   user_counts,

        -- initialize our variables
join   (select @user_rank := 0, @current_username := 'abcdefg') r

order by username, ucount desc

Then wrap this in our final select, making sure to only display those rows with a ranking of '1' ... pulling it all together into a single query we have:

select id,
       uid,
       ucount as 'count',
       username,
       track,
       title,
       time

from   (select id,
               uid,
               ucount,
               username,
               track,
               title,
               time,
               @user_rank        := if(@current_username = username, @user_rank:=@user_rank+1, 1) as user_rank,
               @current_username := username

        from   (select tracks.id,
                       tracks.uid,
                       count(*) as ucount,
                       users.username,
                       views.track,
                       tracks.title,
                       tracks.time

                from    tracks
                join    views
                on      views.track = tracks.id

                join    users
                on      users.idu = tracks.uid

                group by tracks.id,
                         tracks.uid,
                         users.username,
                         views.track,
                         tracks.title,
                         tracks.time) user_counts

                -- initialize our variables
        join   (select @user_rank := 0, @current_username := 'abcdefg') r

        order by username, ucount desc) dt

where   user_rank = 1

order by ucount desc, username

And the results:

id uid count username      track title              time
-- --- ----- ------------- ----- ------------------ -------------------
55 567     3 TrainingPuppy    55 No love liers      2016-10-11 22:57:51
 2  15     1 SewingButtons     2 Worf is in the air 2016-02-11 22:57:35

Some fiddles:

• MySQL 5.6
• MySQL 5.7
• MariaDB 10.2

NOTE: If a given username has the same max(count) for more than one track/title, this solution will only display one record; to display multiple records would require a tweak to ensure said records receive the same ranking (ie, user_rank = 1).