Most Wizards work best from the back lines.  Unfortunately, there might not be enough, or even any, companions to handle all that the world throws at you.  In comes the Master Summoner who reaches across the planes to bring creatures to his/ her aid.  Horde of gnolls charging at you from across the battle field?  Say hello to my Wind Elemental!  A giant just smashed your Barbarian with a well aimed boulder from the other side of the valley?  Here's a few Giant Eagles to tie them up while he gets back on his feet.

Summoners can bring all sorts of creatures to their aid.  And as they grow in power, so to does the aid they are able to summon.

Summoning Savant

Beginning when you select this school at 2nd level, the gold and time you must spend to copy a spell with the summoning tag into your spellbook is halved.  

I Summon, I Don't Create

Upon choosing this subclass at level 2, you GAIN access to additional spells, but this comes at a cost.  You LOSE access to certain spells as well.  By choosing this subclass, you gain the ability to learn any spell with the SUMMONING tag (from any spell list) but you lose the ability to learn any spell with the CREATION tag (There are two exceptions - 1. You can cast Light as a racial ability.  2. You can still cast Wish.).  For all spells gained through this feature, they count as Wizard spells for you.  This means you can use your Wizard casting ability for any DC checks.

Powerful Summoner

Starting at 6th level, when you cast a spell that summons a creature, the summoned creatures are summoned with maximum HP.  Your summoned familiar from the Find Familiar spell now has double the max HP.  In addition, the duration for all summoned creatures is doubled.

Focused Summoning

Beginning at 10th level, concentration checks made to maintain your summoned creatures are made with advantage. 

Master Summoner

Starting at 14th level, when you cast a spell that allows you to summon a creature at higher level, you can choose to either summon a creature of greater CR, or increase the number of creatures you summon. Some spells allow you to do one or the other, but this allows you to choose which one you would rather do.  Use the following formula for you calculations, unless the spell description states other wise. 

You can summon creatures of 1 additional CR per 1 level of spell over it's original spell slot. (Example: The 3rd level spell Conjure Animals allows you to summon a beast of CR 2 in the spells original form.  With this feature, if cast at a level 4, the CR max increase to 3.  If cast at level 5, the CR max increase to 4 or you can choose to follow the spells original description and summon additional creatures at CR 2 or lower with this pattern continuing through 9th level)

Your second option, is to summon 1 additional creature at the cost of 2 spell levels higher per creature above the original spell slot. (Example: The 5th level spell Conjure Elemental allows you to summon 1 creature of CR 5 or lower.  With this feature, if cast at level 6, you can summon a creature of CR 6 or lower.  If cast at level 7, you can choose to summon 2 creatures of CR 5 or lower or you can choose to follow the spells original description and summon 1 creature of CR 7 or lower with this patter continuing through 9th level)

This feature can only be used if the spell can be cast at higher levels.  The only exception is Conjure Celestial  which can not be cast at 8th level.