NOW you will learn why it was called the "Great Age":
Europe was, naturally, filled with warfare. As always.
Scotland emerged into the new century out of several bloody feuds degenerating into a civil war. Luckily, King Jacob VI was an able administrator. He rebuilt the economy, converted Northern Ireland, fought back an English incursion and founded Scotlands first colony. No doubt, he was one of the Greats, though he rarely was named such - more often, he was called Jacob the Just, or Jacob the Bearded. The English lost the Irish War to him (in part due to Jacob's declaration of religious tolerance), allowing Scotland to grab Southern Ireland as well.
The Lisbon Alliance collapsed during that time, due to the Great Indian Ocean War which pitted Netherlands, Castille and France against England and Portugal. Most fighting took place in Indian Ocean territories and other colonies, but some spilled over to the Continent, such as the Dutch-Castillian victory at the Tagus Delta over the main Portuguese fleet (bolstered by the English) and the Castillian siege of Lisbon, barely fought back by the Portuguese forces.
Henri VI, named, as one might expect, the Great had all intentions to make France the new Greatest Power, thinking the Jagiellons to be decaying. The First Lithuanian War persuaded him in the need of a different policy. He allied with the Jagiellons, and prepared for a new, grandiose campaign. The fate of France and Europe, in his opinion, was to be decided in Italy. His campaigns had Papal support at first, as he ousted the Guise dynasty from Italy city by city in a three-year campaign. After keeping all the territory he gained, though, he antagonized the Pope and Venice. This started the Sixth Italian - or Second Lithuanian - War (1719-1724). During it, French forces, after a lengthy siege, looted Rome itself, winning Henri the hatred of all remaining French Catholics and those abroad, and even some Protestants protested the rape of Rome - including Leonard dAuttervile, one of the chief humanitarians of the 18th century who compared Henri with Alarich. Soon after Rome was taken, Venice launched yet another counteroffensive that threatened Henri VIs supply lines. The Jagiellon Empire entered the war then, and the Polish-Hungarian-Bohemian-Austrian forces, led by the very old Marshall Krapiwecki himself, besieged Venice. After taking the city, Krapiwecki had to confront a Venetian-Papal-Swiss mercenary-Italian rebel force at Mantua in 1723. That battle was thought by some to be Krapiweckis greatest triumph - and his last one. The entire Venetian-Swiss forces were utterly crushed by a relatively small detachment of Krapiweckis forces, while the rest kept down a rebellion in Venice and prevented the other forces from getting to the Venetian lines. Krapiwecki, unfortunately, was wounded in the battle and died on his way to meet Henri VI. Soon after, his army was recalled - the anti-Jagiellon Coalition resumed its assault, and though the German princes were distracted to the western front, Swedes and Russians were attacking once again. The Polish forces had just one more grand triumph during this war, though, having seized Helsinki in a surprise attack. Henri VI was fought to a standstill at Saarbrucken, but was not dismayed as he cared little for Rhine.
The Treaty of Vatican had France take all Italian lands, Poland take the Venetian lands minus Lombardia (which became independant), and status quo elsewhere. The destruction of the Venetian Republic and the Italian Kingdom was momentous and ground-breaking, as it undid much of the balance in Italy.
In 1730, the North German princes formed a new league - the Hamburg, or Protestant, league. The Protestant Confederation arose from it soon after, under the leadership of Palatinator Adolph the Great who also was the hero of Saarbrucken. Truth be said, he was an average commander, but a brilliant diplomat and statesman.
Sweden and Denmark-Norway were pretty much left out in the Great monarch scene, yet those were still the times of prospering trade, improving relations and so on, that made Scandinavia the most peaceful part of the world - if one does not count Finland... but more on that under the Third Lithuanian War.
The Jagiellon Empire was ruled by Valdemar III, who hoped to make himself another one of "the Greats". Unfortunately, his surname was "the Fat", and even that was merciful to him... Valdemar III was not as incompetent as is popularily believed, but lack of luck led to his defeat in the Third Lithuanian War.
Russia and Ottoman Empire were both working on reorgonizing and modernizing themselves. Unfortunately, while the former received assistance from its traditional English and Danish allies, the latter only received (occasional) support from Henri VI who was wary of Aragon threatening his positions in Italy by seizing more of North Africa. Though both were modernizing, under Suleyman II and Mikhail III respectively (both of them "Great"), they were doing so differently - Russia by inviting foreign, primarily English and Danish, nobles and scholars, while the Ottomans, by trying to adopt the foreign advances almost by themselves. Russia was advancing more slowly and less radically, but did not stop, while the Ottoman Empire encountered iternal and external differences, as Aragonese and Persian forces begun assaulting the Empire again and the Janissaries were constantly mutineeing and rebelling in Constantinople itself...
Third Lithuanian War marked the end of the Jagiellon supremacy in Eastern Europe, though failed to break up the Empire. The war, naturally, had little to do with Lithuania, save for the fact that some fighting took place there as well. It started in 1743, shortly after Mikhail III the Great's death - him having achieved a reorganization of the Russian military and political structure, an emancipation of the serfs and several victorious wars, including the Crimean War against the Turks. His son, Mikhail IV, was determined to defeat the only "enemy of the Rus" whom his father did not defeat - the Poles. Mikhail III worked tirelessly to form a powerful coalition of Russia, Sweden, Denmark-Norway, England, Protestant Confederation and even France, after Mikhail III pointed out that Polish Venice is an exellent location from which to invade French holdings in Italy. Bavaria strayed away, though, fearing the "Orthodox-Protestant Conspiracy", and even allied with the Poles.
Mikhail IV was very proud of the army he commanded during the Crimean War, he saw it to be just as good - if not better - then that of France, and was very eager to test it out. So, when in July 1743 a Finnish rebellion begun in Helsinki, Mikhail was quick to "find" evidence that the Jagiellons were at least distantly connected to it. That was a violation of the Treaty of Vatican, and thus Sweden had to declare war on the Jagiellon Empire. Poles found out the hard way that they had only two allies left, Bavaria and Aragon, and the latter couldn't do much but tie up some French forces.
The Russian army was, naturally, not on the level of the French one, but a lot better then what the Polish commanders expected. This horrible underestimation of the enemy has costed the Polish army several near-catastrophic and fully-catastrophic defeats: at Rovno, Revel, Riga, Kiev, Kherson, Uman and Orsha, in the first two years of the war. However, the Poles recovered from this later on. Meanwhile, the Polish forces landed in Helsinki again, to assist Vaako and his rebels.The rebellion was spreading through Finland, and the Swedish forces were totally unprepared for any war, especially for a guerrila one.
The French army tried to seize Venice, but Lombardy too allied with the Poles after the French tried to move through its lands, and thus General Rousselle was forced back by a Jagiellon-Lombardian-Bavaria army. A second French expedition seized Milan, but failed to advance into Venice due to supply reasons. The Franco-Protestant forces broke through Bavarian lines at Kaiserslauten (in 1747) and invaded Bavaria itself, pillaging the countryside. Much as Adolph was not interested in getting a sizeable Catholic minority, he was bent on unifying at least those parts of Germany that were not under Polish rule.
From 1748 on, the Jagiellons attempted to regain initiative. They stopped the Russian advance on the river Venta in Latvia, although elsewhere, they lost huge amounts of territory, and the remaining Cossacks were rebelling. Indeed, much of southeastern and southern Polish possessions were as good as lost. And lost they were. Steadily, now with Russian support, the Swedes were pushing back the Finnish rebels, and the rebelllion was crushed by 1751. Vaako made a very good martyr, though, and since then rebellions in Finland will continue until it finally achieved independance... but more on that MUCH later on.
Bavaria utterly collapsed in 1752, after its king died. As per the agreement, Protestant Confederation now annexed Bavaria as well. In return, it signed an alliance with France and agreed to divide Switzerland with it in the near future. Aragon left the war by then. Bohemian and Austrian Protestants were rebelling. Horrified at the sight of his crumbling empire, Valdemar abdicated and fled, without naming a successor. The Council of Regents was assembled, and signed peace with the anti-Jagiellon coalition. Jagiellon Empire was preserved due to Arkadiusz' diplomatic skills, but the Treaty of Lublin led to loss of Pommerania (to Protestant Confederation), Venice (to France), Livonia, much of Ukraine and all of the remaining "Greatrussian" territories (ethnic Russian territory, much of the OTL European Russian Federation) (to Russia, obviously enough). Protestant Confederation has now unified all the few remaining independant German states, and declared itself Germany, abolishing the Holy Roman Empire. This new Germany was a parliamentary monarchy (much like OTL England at the same time), and not as much military-based as it was city-based and industry-based.
The Jagiellon Empire was badly wrecked, yet its four kingdoms remained unified, for the moment at least. Poland was the only Catholic majority kingdom of the Empire, and Catholicism's state-imposed predominance seemed to prove that it was, indeed, the Polish Empire. Severe strife came after the war, as the Regents fought over the country, and the Lithuanian Arkadiusz, the "Jagiellon" (note: Jagiellon Dynasty is over, but the Empire is still called Jagiellon for simplicity's sake) representative to the Lublin negotiations, emerged from it after five years as the new king. Now, Arkadiusz has definitely deserved the title of "the Great", having reorganized the empire, established religious tolerance and fortified it, in its new compact state, allowing it to survive until the Second Great War.