A Wizard of the Focused Mind is particularly good at staying focused on a task.   They delight in spells that require concentration and have abilities that aid them in doing this. They can enter several different states of mind that allow them to exceed the normal limits of spell-casting.  They can only be in one mental state at a time, except where otherwise noted.

Focused Savant

Beginning when you select this school at 2nd level, the gold and time you must spend to copy any spell that requires concentration into your spell book is halved.

Split Concentration

As a bonus action, you can enter the "Split Concentration" state of mind.  While in this state, you can not take any bonus actions or any reactions.   Entering this state ends any other state of mind.    This state of mind lasts until a concentration spell you cast ends for any reason - Counterspell, Dispell, failed concentration check, you end it early, etc. etc.

In Split Concentration, you can concentrate on up to two different spells at once (casting a new spell no longer ends the old one).  In addition, when concentrating on a single spell, you have advantage on all saving throws to maintain concentration.  If you have two spells up and you have to make a saving throw to maintain concentration, you suffer disadvantage.  If you fail the disadvantaged roll, both spells end.

 You can do this once per your Intelligence Stat Modifier.  This resets after a long rest.
 

Long Haul Caster

Upon reaching sixth level, as a bonus action just before casting a concentration spell, you can enter a state of  "Enlightened Time".   Entering this state ends any other state of mind.   

While in this state you can cast only one spell. Attempting to cast another spell takes you out of this state.   Attempting to take a bonus action or a reaction requires you to make a concentration check or end this state of mind but will only end your spell if the normal duration has passed.

While in Enlightened Time, time has no meaning and you ignore normal limits on how long you can maintain a spell.   You can keep the spell up until you fall asleep or take a short or long rest.  However, this process is tiring.  If you extend a spell for longer than twice it's original concentration, you gain one level of exhaustion (+1 level).   After that, every hour you attempt to extend it requires a concentration check DC = 12 + spell level.  Failure means you gain another level of exhaustion.  

You can enter Enlightened Time once per short rest, but it takes magic or a long rest to remove a level of exhaustion.

 

Iron Will

After reaching 10th level, your will has strengthened considerably.  The effect depends on what state of mind you are in.

If you are in your normal state of mind (concentrating on a single spell for the normal duration), nothing short of death can break your concentration. You no longer need to make saving throws when you take damage or in other circumstances.   Even should you fall asleep or be otherwise incapacitated, your spell continues for it's maximum normal duration.  

If you are in another state of mind, (i.e. Split or Enlightened) you now have advantage on all concentration checks.  Please note, if you are in advantage does not stack and cancels out with disadvantage.   So once you have 10th level, in Split Concentration results in Advantage for a single spell, and a single normal roll (no advantage or disadvantage) for concentrating on two spells.

Dual Concentration

Starting at 14th level, your gain the most powerful state of mind, "Dual concentration", similar, but better than "Split Concentration". This state takes a bonus action to enter, and can only be done once (before a long rest).  It does not count as one of Split Concentration uses.

Dual Concentration entails all the benefits (and disadvantages) of normal Split Concentration, with a powerful additional ability that only lasts for the first round of the state of mind.  In that first round, your ability to concentrate is so great that you can actually cast two Wizard concentration spells in a single action.  This is an exception to the rule that states "You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action."

Both spells must take up a slot of 4th level or lower.  You must take a long rest before doing this again.  Also, only spells that have concentration as their duration (regardless of the time limit) can be used.