This game is awesome and fun with every match a new obstacle to overcome. Everyone starts every new match at level one with no items and must build up their champion over the course of the 15 minute - 1 hour long match in a 5vs5 team fight.
This game gives you lots of options from being a tank and taking a death for the team to being the Attack Damage Carry who kills everyone and carries the team.
On Summoner's Rift you play a competitive 5vs5, on a three lane map with monsters and buffs, with the goal of destroying the three turrets/towers that guard each lane to get to their Nexus which you ultimately want to destroy. With over a hundred champions and 6 roles to play; Assassin, Attack Damage Carry(ADC), Jungler, Ability Power Carry(APC), Support and Tank, and tons of items you will find every game a challenge.
On the slightly more relaxed Twisted Treelines with only 3vs3, you play a semi-no-role kinda game, with all the same fun objectives of Summoners Rift of taking out your enemies turrets/towers to get to the nexus.
Two more modes, Dominion and ARAM add more flavor. Dominion you try to take and maintain control over five points that slowly negate the health of your enemies Nexus as long as you control them. ARAM aka All Random All Mid, is a mode where your champion is randomly selected for you and you all go down the middle lane trying to destroy the turrets and your enemies Nexus.
On top of the modes and wide champion selection League of Legends has an expansive lore that even comes up in the matches with certain champions sayings changing if a certain champion from their lore is on the opposing team.
i.e. the champion Rengar says something different upon activating his ultimate if the champion Kha'Zix(his enemy according to their lore) is nearby.
You will have lots of fun reading lore and listening to the champions say stuff in matches.
I rate this game 9 which I truly think it is worthy of.