Changes in the SUMMONER throughout the levels

First of all, The Lore:
Understand that both the Summoner and Scholar are first and foremost Arcanists. Arcanists (a DoT Damage Mage and backup healer) that dabbled in summoning with Carbuncle, and as they grew in knowlege and power split off and strengthened one side of Summoning or the other, either healing or damage.

The basis for the Summoner job itself...is Arcanist focusing on Summoning abilities for damage.

That's the lore... the reality of the game however... and how it actually plays give the Summoner two primary focuses it excels at. AoE damage on multiple targets, and excellent solo abilities, (capable of soloing Boss mobs in FATEs).

While we all know its primary attacks are Damage over Time spells, what is not known as well is how much AoE (Area of Effect) damage they put out and how... (regardless of level). This actually becomes their greatest strength in a party and then becomes the singular thing they excel better than any other Job at the highest levels.

So without further delay... Tactically from my perspective the largest change comes at level 52 in this class when it comes onto its own.

From level 1-29:
Most of your skills are solo based and you don't have any good AoEs unless you Sub Blizzard 2 and spam it as an AoE. Generally tactics at this level for me were Bio 2, Miasma, and Bio on single targets along with the using Life Steal from Aetherstacks during boss mob battles simply for the damage... I found it near impossible to run out of MP on single targets even prior to that...

For the level 15-20th level dungeons
Standard tactics for multiple mobs... were... Bio... one on each mob, (quick cast time on it made it doable)... then stepping in and spamming Bliz 2 from BLM, and using Life Steal on the last target. Early on if they didn't drop too fast you could actually do Bio and Miasma on each and then step in with the Bliz 2 spam, but rarely was this the case. Then on the last target using Life Steal to suck your mana back and using Aetherflow to instantly have you back up to nearly full.

Level 30-45:
Things change at this level... now you're using Bane... which spreads your DoTs to all targets for an AoE... Now you can start using all of your DoTs... Bio, Miasma, and Bio 2... then you hit Bane and spread the DoT when against multiple enemies in Dungeons. Then... step in and Spam Bliz 2 on multiple mobs... (which adds about 30% more damage to your already spread DoT on the mobs, taking down large groups of enemies fast).
Plus you can Use Rouse on your pet at level 40 for a nice boost in damage.

(At this level due to your Bane and Bliz 2 you are actually doing just as much AoE damage as a Black Mage, potentially even more. aka Potency wise (Bio I) 40 + (Miasma) 35 + (Bio II) 35 + plus another 50 potency per 2 seconds from Bliz 2... for about 175 potency per tick AoE damage)

Thus does Garuda's Contagion start to become noticeably important.

On Single Targets and Boss Mobs, you now add Fester to your rotation of Bio, Miasma, Bio2, when combined with Rouse, you can kick in major damage, especially if you've got Archer to level 15 and have Raging Strikes... this combo alone on Boss Mobs at that level can be very damaging. You no longer need to waste Life Steal when you don't need any MP or HP.
Fester works much better.

Obviously here, I've broken it down into Single Target scenario, and Multi-target scenario. Because you use different tactics for one vs the other.

Level 46-51:
Here you gain two more DoTs in Miasma II and ShadowFlare. Both are designed to stack with your other DoTs... I admit due to the mobile nature of combat Shadowflare can end up Situational as its a placed effect. But when all of your DoTs are stacked togather AND you're spamming Bliz 2, the AoE damage you start to put out is pretty sizable. It's actually close to 860 Potency after all ticks from DoTs...
Add Bliz 2 plus Bane DoTs gets pretty nasty on Large Groups of trash mobs. Throw in and Garuda AoE Wind (Enkindle) attack and you start to do some serious AoE damage.

(Note though... DoTs do not appear in the Battle chat log, you'll have to test it on equal level Mobs and watch them directly to see the numbers pop on what your stacked DoTs tick, at level 60 and i250 mine are at 1700 damage per tick with just Bio, Bio2, and Miasma.... Miasma 2 and Shadowflare push this to 2000-2500 per tick)

Not much changes with regard to single target and Boss Mobs... with the exception of Rouse and Spur... and kicking in Enkindle allows your pet to make a 1000+ damage attack, so its about like an Extra Fester. Not to mention mine (Garuda) at those levels was generally hitting for about 500+ damage per normal attack under the influence.

Its the next levels that are the big change... and where the Summoner finally becomes an FFXI Summoner... and gains the ability to wipe out entire crowds of mobs in seconds.

Level 52
Painflare now gets added to your AoE rotation. So now, on top of your AoE Bane DoTs... You add another more powerful AoE attack. So now when clearing large crowds of mobs... you use...
Example
Quickcast + Shadowflare>Bio II>Miasma>Bio I>Contagion>Painflare>Bane>Miasma II>Rouse+Spur+Enkindle>
.. then step in and spam Bliz 2.

Level 54
You now gain Ruin III, a very powerful single target attack, so now on your single target boss mob rotation gets much more powerful,
Example:
Quickcast + Shadowflare>Bio2>Miasma>Bio1>Contagion>
Fester>Ruin3>Ruin3>Fester>Ruin3>Ruin3>Fester...
And you can now double tap a quick single target bust using Ruin 3 + Ruin 2 in rapid succession. Done right it gives a kind of Ba-Pow two shot quick hit. For a 280 total potency quick attack. Kind of like a Red Mage's Dual Casting.

Level 56-60
Tri-Disaster... the biggest AoE Mob destroyer in your arsonel... It's not an AoE attack in and of itself its an enabler... it allows you to literally insta cast large amounts of DoTs at once... so EXAMPLE...
Quickcast + Shadowflare>Tri-Disaster>Contagion>
Painflare>Bane>Painflare>
Rouse+Spur+Enkindle>Dreadwyrm Trance>Deathflare
...almost all of these abilities are insta-cast. No casting time, allowing you to blow your stacks and wipe out a large 6-10 mob spread incredibly fast.

The Summoner, literally begins and ends as an AoE mage capable of doing large amounts of damage to multiple mobs and trash mobs in dungeons. Thus do you see where the true strength of the class/job lays and the way this changes throughout the levels.

It is at level 60 that it truly begins to look and play just like a True Final Fantasy Summoner wiping out large crowds of mobs.