Also, what are some good online primary sources for the battle? Thank you
To understand the battle of Kursk, we need to go into the events that lead to the formation of the salient as that is crucial to the understanding of motives and actions.
Background
After the fall of Stalingrad, the Soviet winter offensive put the Wehrmacht on a strategic and operational defense along the Eastern Front. Soviet forces managed to force a 200 km long gap between Army Group B and Army Group Don. STAVKA (Stalin), emboldened by the success at Stalingrad pushed on with the aim of seizing the Dnieper crossings and encircling Army Group Don and replicating the success of Stalingrad.
On the German front, Hitler as usual wanted to hold all territory, but Manstein convinced him that to do this would be suicidal and lead to the sure destruction of Army Group Don. Hitler for once listened to his finest commander and gave Manstein a free hand.
Manstein then delivered the 'miracle at Kharkov' (in my opinion one of the finest genius level maneuvers in all military history) where using the "Schlagen aus der Nacchand" (Strike from the back of the hand) maneuver , he shortened his front, allowed the Russians to over extend, and despite facing overwhelming superiority in numbers, took Kharkov (or should I say retook it). This had a hidden positive effect, it spoiled the attack STAVKA planned on Army Group Centre and allowed them time to regroup.
At the end of Manstein's genius 3rd battle of Kharkov, the frontlines had been drawn and the Kursk salient formed.
German Position and Strategic Objectives - OKH thought that, Soviet reserves had been completely bled and one more summer campaign would finish the final reserves of manpower the Soviets had. This was what Hitler and Kurt Zietzler (the chief of the OKH) thought. Manstein (and Guderian) thought otherwise, they felt that German manpower was almost depleted and another offensive would mean the end of German manpower reserves. After seeing the benefits of a strategic defense, using mobility and shortened lines to counter attack Soviet spearheads, he proposed that the German lines be shortened and the Wehrmacht go on the strategic defensive.
Manstein proposed a sort of an Eastern version of the Von Schifelen plan. Wait for the Soviet Offensive, draw them into operational space and counter attack on their deep flanks - essentially replicate his maneuvers at Kharkov. Hitler would as expected, have none of it.
With hindsight, Manstein was proved right. Soviet dispositions, STAVKA reports all establish the fact that the Soviets considered the Southern theatre the most vital and were indeed planning on a counter attack in this region (as predicted by Manstein).
Hitler feared a Western offensive (in which he was proved correct) and wanted to restore equilibrium in the East, so as to free troops to defend in the West. He did not want to wait till the Soviets went on the offensive, but he wanted to take the offensive before the Soviets did.
Zitadelle (Kursk operation) was originally planned for April, but raptistuta (spring thaw) meant that it had to be postponed for the summer. By May, senior officers in the OKH after seeing the recon photos of defence in layer had their own doubts, but Hitlers solution was...to brute force his way in with the new Panthers & Tigers which he hoped would turn the tide in his favour.
Manstein again came to the rescue and suggested that the Wehrmacht, instead of attacking via pincer movements in the base of the salient, could attack frontally as he felt that the front was only lightly defended. Hitler again vetoed the idea.
The overall objective of Zitadelle was merely to reduce the salient, encircle two whole fronts and restore the equilibrium on the Eastern front.
How was the third battle of Kharkov relevant here? Manstein proved that a strategic defense worked very well and that forcing the Soviets into over extending themselves and counterattacking at one chosen Schwerpunkt would help the Wehrmacht nullify the Soviet advantage in numbers.
Hitler of course would have none of it.
The Soviet position and objectives
The STAVKA (Stalin) wanted to go on the offensive in the Kursk salient, but Zhukov convinced him of the dangers of such an offensive (Kharkov would have been a real time reminder to Stalin), and suggested they go on the defensive.
Thanks to some good intel and brilliant maskriovka, they created a 3 tier defence structure. Their plan was simple, amass reserves, exhaust the Germans, unfold their counter offensive.
Their strategic objective was simple - wear out the Germans before launching their massive counter offensive.
How was the third battle of Kharkov relevant here? It helped buffer Zhukov's claim that the Wehrmacht was still not a spent force (as Stalin believed it to be) and they could still fight against overwhelming odds. That going on the strategic defensive here was the prudent course of action.
Stalin by this stage was amenable to listen to a few of his senior commanders and listened to Zhukov.
The rest as they say is history.
Unfortunately I am not in a position to recommend online sources, but books I can refer you to.
Edit - Added a few more details.