In addition to what sir jib said above this response ...

[Please refer to the image above] : As you can see, in the first box, that's your Summoning Level (Level 10 in the Image) and below that is your Summoning Level Experience Bar (1/180 in the image) .. For you to increase your bar, you must cultivate your available summons, each Hexagon will add 1 point to your Experience Bar and when you reach the certain number needed, you will go level up and unlock the other summons for you to cultivate .. You don't need to max all you summons, and there are some techniques on how to level up your Summoning without needing too much Unbounds, try to look for some Guide or Threads here in forums and you may get some tricks about the Cultivations ..

..(sorry for the image, Kirin went out to grab some lunch xD)