I am lithuanian, but unfortunately not a historian. So the answer might not hold up to the subs standarts. I apologise in advance.

At the beggining of the 14th century Grand Duke Gediminas became the ruller of the country. He saw that the country is far behind western Europe in terms of technology and culture and sought to fix this problem. The reason he stood out in lithuanian history, is because as lithuanians like to say: he ruled by the feather rather than the sword - tried to use diplomacy rather than warfare to achieve his goals:

1. A lot of the lands added to lithuania by him, were gained by marrying his children to belarusian rulers
2. He moved the capital to Vilnius and wrote numerous letters to western cities "advertising" Vilnius, asking artists, carpenters, builders, etc. to come work here. Thanks to him the city quickly became a cultural beacon in eastern europe, akin to the likes of prague.

After his passing, in 1341 his son Vytenis took over for a about 4 years, his rulling wasn't of much consequence as in 1345 he was overthrown by his two brothers Algirdas and Kestutis.

Although Algirdas became the actual ruler, they split up responsibilities, which allowed the to succesfuly fight on two fronts:

Kestutis was resposible for figting the crusaders on the western front. And although he didn't gain much land, he also didn't loose it, which was basically attributed to the fact that lithuanian abused their knowledge of the surounding forests and swamps to outmaneuver the more heavily armed western knights and avoid unfarovable encounters.

On the eastern front Algirdas focused on conquering slavik lands by warfare and wedlock, the profits and manpower obtained by his quests funded his brothers struggle against the chirstians.

After Algirdas's death in 1377 his son Jogaila came into power and incarcerated Kestutis and his son Vytautas after Kestutis tired to overthrow him for negotiating with the crusdares. Kestutis died in prison and Vytautas escaped to Prusia where he was suported by the crusaders to fight Jogaila and in a few years betrayed them and fled back to Lithunia after reaching an agreement with Jogaila.

In 1384 Jogaila was offered the hand of the current queen of Poland Jadvyga, Lithunia accepted christianity, the two contries were united under his rulling and he appointed Vytautas as the submonarch of Lithunia. Although the crusaders lost their claim for lithuanian lands, it was only in 1410 suffered a massive deafeat against the lithuanian-polish alliance which is attributed to Vytautas outmaneuvering and baiting the enemy into an ambush. The defeat lead to peace treatys int 1411 and 1422 which ended the conflict against the crusaders.

On the eastern front Vytautas gained for slavik lands and extended the lithuanian border to the black sea by succesfuly defeating the local tatars, getting beaten by the Golden Horde in 1399 and establishing peace with them in 1418. He died in 1430 after several attempts to get crowned as king of Lithuania.

His time of ruling is the peak of Lithuanias power.

After his death, the polish cultural and political influence began growing rapidly in lithuania, during the coming ages, Lithuania and Poland grew closer together. The monarchy became the second power to the parliament which consisted mostly of self-serving lords, easily bribed by other countries. And the lithuanian-polish alliance dissapeared after Prusia, Austria and Russia cooperated in taking the country appart.

I don't want to be too vague, that's why my story only starts with Gediminas but i can do more research when i get back home. I'm sorry for lack of detail but i'm at work and would need to get back home for more details and sources, but please followup and i'll try my best to provide what i can.

Follow up question: Was Lithuania a pagan nation?