You can check your current rank and rank level at the top of the game's main screen, next to your username. In this case, we're on the Lieutenant-2 rank level 3.
Each rank is composed of a number of levels, as shown below:
- Private: 1 Level
- Soldier: 1 Level
- Private First Class: 2 Levels
- Corporal: 4 Levels
- Sergeant: 4 Levels
- Non-Com. Officer: 4 Levels
- Lieutenant-2: 4 Levels
- Lieutenant-1: 8 Levels
- Captain: 8 Levels
- Major: 8 Levels
- Lieutenant Colonel: 8 Levels
- Colonel: 8 Levels
- Brigadier General: 16 Levels
- Major General: 16 Levels
- Lieutenant General: 32 Levels
- General: 32 Levels
- General of the Army: 32 Levels
- Commander in Chief: 64 Levels
Here's how it works: At the end of a battle, your score is added to your total profile score. Once you accumulate enough points to level up within your current rank, you'll move to the next level of that rank. If there is no higher level within your current rank, you'll progress to the next rank altogether.
This means that if you're currently at Lieutenant-2, and since this rank includes 4 levels, you'll need to progress through all of them before advancing to Lieutenant-1.
Also, you get prizes when you increase your rank! There are different rewards for each rank, including fuel, coins, and diamonds.