The Roster Tab shows a list of your dragons. Here, you can level them up, train and pet them.
The dragons with a little sword symbol on their profile picture are currently in a battle team. You can have up to 5 different battle teams. The roster space will increase with your levels but you can upgrade it faster by using . (250 /purchase)Select the 'Edit team' button to view the dragons in your teams and change them. The button with 2 arrows will order your dragons by Rarity, Power or Color, but the dragons in a battle team will always be the first to show up. The current maximum number of slots is 180.
Special dragons uncollected (Trust Points not max) won't count in the limit, but sheep will.
Book of Dragons section
Here, you will see all the dragons ordered by their species or types. There are currently 179 dragons in the game available to battle. Tap on them to see their maxed stats and ability and their availability. If a dragon you have can be breed, the availability will show you a BREED icon. Clicking on it will show the parthers you can use to obtain another one. Unobtained dragons having the Breedery symbol means you own the parthers that can have the dragon as offspring. Collecting dragons from a species or group gives you and chests as rewards.