Rankings
Are you interested in how your airline is faring compared to the others? If so, click on the "Reports" button at the top. There are four types of rankings in AM: Airline Rankings, Airline Rankings by Continent, Aircraft Rankings, and Alliance Rankings.
Airline Rankings
This is the default page of "rankings". Here you can see the ranking of airlines listed according to their value. The airline value is the the net worth of the airline, which is calculated based on cash and the book values of the aircrafts the airline owns. On the same page, you can see the airline code and player's id, which would be useful when dealing with each other.
Clicking on the name of a airline would bring you the details of the airline. The information page includes the fleet, the alliance the airline is in, a list of gates, a route map, and some statistics (daily passenger, longest route, most fuel use) of the airline. From there, you could click on the airport codes to view the detail of the airports the airline is operating in.
Airline Ranking by Continent
Airline Ranking by Continent is the second selection on the rankings page. It enables you to see what rank different airlines are in their regions. Once in your desired continent page, the same features are available from the "airline rankings" page.
Aircraft Rankings
Aircraft Rankings is the third selection on the rankings page. Here you can see the types of aircraft ranked by the total number currently in service throughout the game. This ranking is useful as higher aircraft popularity may be an indication of profitability, assuming you trust other owners to maximize profits.
Clicking on a type of aircraft displays a list of airlines that own it along with the quantity each airline owns.
Alliance Rankings
This is the fourth selection in the rankings page. You can check the ranking of your alliance here. They are listed by total net worth in descending order.