Question: What Duchy founded by the Lithuanians, was Kestutis the Grand Duck of? 

Context articles: History of Lithuania
Metropolitanate of Lithuania
Lipka Tatars
Palemonids
Birutė
Lithuanian Chronicles
Muscovite–Lithuanian Wars
Lithuanian–Muscovite War (1368–72)
Lithuanian Crusade
Grand Duchy of Lithuania

The history of Lithuania dates back to settlements founded many thousands of years ago , but the first written record of the name for the country dates back to 1009 AD.
 Lithuanians, one of the Baltic peoples, later conquered neighboring lands and established the Grand Duchy of Lithuania in the 13th century (and also a short-lived Kingdom of Lithuania).
 The Grand Duchy was a successful and lasting warrior state.
 It remained fiercely independent and was one of the last areas of Europe to adopt Christianity (beginning in the 14th century).
 A formidable power, it became the largest state in Europe in the 15th century through the conquest of large groups of East Slavs who resided in Ruthenia.
 In 1385, the Grand Duchy formed a dynastic union with Poland through the Union of Krewo.
 Later, the Union of Lublin (1569) created the Polish–Lithuanian Commonwealth that lasted until 1795, when the last of the Partitions of Poland erased both Lithuania and Poland from the political map.
 Afterward, the Lithuanians lived under the rule of the Russian Empire until the 20th century.
The Metropolitanate of Lithuania was a short-lived metropolitanate of the Orthodox Church in the 14th century.
 Created between 1315 and 1317, it had only two metropolitans and was discontinued in 1371.
 Its establishment was part of the entry of the Grand Duchy of Lithuania into the rivalry for the religious control of the Rus' principalities between Galicia–Volhynia, the Principality of Tver, and the Grand Duchy of Moscow.
 The Byzantine Empire, seat of the Patriarch of Constantinople, generally preferred a united Metropolitanate of Kiev and all Rus' and was reluctant to divide its authority.
 Therefore, whenever possible, the Byzantium would unite the metropolitanates.
 Facing opposition to actual physical division of the metropolitanates, the Lithuanians employed additional tactics: promotion of their own candidates to the seat of the Metropolitan of Kiev and all Rus'.
 By the 1440s however, the final years of the Byzantine Empire, the Grand Duchy of Moscow had effectively won the dispute and became the new spiritual center of the Orthodox tradition in Eastern Europe.
The Lipka Tatars (also known as Lithuanian Tatars, Polish Tatars, "Lipkowie", "Lipcani" or "Muślimi") are a group of Tatars who originally settled in the Grand Duchy of Lithuania at the beginning of the 14th century.
 The first settlers tried to preserve their shamanistic religion and sought asylum amongst the non-Christian Lithuanians.
 Towards the end of the 14th century, another wave of Tatars – this time, Muslims, were invited into the Grand Duchy by Vytautas the Great.
 These Tatars first settled in Lithuania proper around Vilnius, Trakai, Hrodna and Kaunas and later spread to other parts of the Grand Duchy that later became part of Polish–Lithuanian Commonwealth.
 These areas comprise present-day Lithuania, Belarus and Poland.
 From the very beginning of their settlement in Lithuania they were known as the Lipka Tatars.
 While maintaining their religion, they united their fate with that of the mainly Christian Polish–Lithuanian Commonwealth.
 From the Battle of Grunwald onwards the Lipka Tatar light cavalry regiments participated in every significant military campaign of Lithuania and Poland.
The Palemonids were a legendary dynasty of Grand Dukes of the Grand Duchy of Lithuania.
 The legend was born in the 15th or 16th century as proof that Lithuanians and the Grand Duchy are of Roman origins.
 Already Jan Długosz (1415–1480) wrote that the Lithuanians were of Roman origin, but did not provide any proof.
 The legend is first recorded in the second edition of the Lithuanian Chronicle produced in the 1530s.
 At the time the Grand Duchy of Lithuania was quarrelling with the Kingdom of Poland, rejecting the claims that Poland had civilized the pagan and barbaric Lithuania.
 The Lithuanian nobility felt a need for the ruling dynasty to show upstanding origins, as the only available chronicles at the time were written by the Teutonic Knights, a long-standing enemy, and depicted Gediminas as a hostler of Vytenis.
Birutė (died 1382) was the second wife of Kęstutis, Grand Duke of Lithuania, and mother of Vytautas the Great.
 There is very little known about Birutė's life, but after her death a strong cult developed among Lithuanians, especially in Samogitia.
The Lithuanian Chronicles (Lithuanian: "Lietuvos metraščiai" ), or Belarusian-Lithuanian Chronicles (Belarusian: Беларуска-літоўскія летапісы ; Russian: Белорусско-литовские летописи ) are three redactions of chronicles compiled in the Grand Duchy of Lithuania.
 All redactions were written in the Ruthenian language and served the needs of Lithuanian patriotism.
 The first edition, compiled in the 1420s, glorified Vytautas the Great and supported his side in power struggles.
 The second redaction, prepared in the first half of the 16th century, started the myth of Lithuanian Roman origin: it gave a fanciful genealogy of Palemon, a noble from the Roman Empire who founded the Grand Duchy.
 This noble origin of Lithuanians was important in cultural rivalry with the Kingdom of Poland.
 The third redaction, known only from the Bychowiec Chronicle, elaborated even further on the legend, but also provided some useful information about the second half of the 15th century.
 The three redactions, the first known historical accounts produced within the Grand Duchy, gave rise to the historiography of Lithuania.
 All medieval historians used these accounts, that survived in 22 known transcriptions, as basis for their publications and some of the myths created in the chronicles persisted even to the beginning of the 20th century.
The Muscovite–Lithuanian Wars (also known as "Russo-Lithuanian Wars", or just either "Muscovite Wars" or "Lithuanian Wars") were a series of wars between the Grand Duchy of Lithuania, allied with the Kingdom of Poland, and the Grand Duchy of Moscow.
 After several defeats at the hands of Ivan III and Vasily III, the Lithuanians were increasingly reliant on Polish aid, which eventually became an important factor in the creation of the Polish–Lithuanian Commonwealth.
 Before the first series of wars in the 15th century, the Grand Duchy of Lithuania had already gained control of a lot of Rus' territories, from Kiev to Mozhaisk, following the collapse of Kievan Rus' after the Mongol invasions.
 Over the course of the series of wars, particularly in the 16th century, the Muscovites were able to expand their domain westwards, taking control of many Rus' lands.
The Lithuanian–Muscovite War encompasses three raids by Algirdas, Grand Duke of Lithuania, to the Grand Duchy of Moscow in 1368, 1370, and 1372.
 Algirdas organized the raids against Dmitry Donskoy in support of the Principality of Tver, chief rival of Moscow.
 In 1368 and 1370, Lithuanians besieged Moscow and burned the posad, but did not succeed in taking the city's Kremlin.
 In 1372, the Lithuanian army was stopped near Lyubutsk where, after a standoff, the Treaty of Lyubutsk was concluded.
 Lithuanians agreed to cease their aid to Tver, which was defeated in 1375.
 Mikhail II of Tver had to acknowledge Dmitry as "elder brother".
The Lithuanian Crusade was a series of campaigns by the Teutonic Order and the Livonian Order, two crusading military orders, to convert the pagan Grand Duchy of Lithuania into Roman Catholicism.
 The Livonian Order settled in Riga in 1202 and the Teutonic Order arrived to Culmerland in 1230s.
 They first conquered other neighboring Baltic tribes – Curonians, Semigallians, Latgalians, Selonians, Old Prussians (see Livonian Crusade and Prussian Crusade).
 The first raid against the Lithuanians and Samogitians was in 1208 and the Orders played a key role in Lithuanian politics, but they were not a direct and immediate threat until 1280s.
 By that time the Grand Duchy of Lithuania was already an established state and could offer organized defense.
 Thus for the next hundred years the Knights organized annual destructive "reise" (raids) into the Samogitian and Lithuanian lands but without great success: border regions in Samogitia and Suvalkija became sparsely inhabited wilderness, but the Order gained very little territory.
 The Grand Duchy finally converted to Christianity in 1386, when Grand Duke Jogaila accepted baptism from Poland before his wedding to reigning Queen Jadwiga and coronation as King of Poland.
 However, the baptism did not stop the crusade as the Order publicly challenged sincerity of the conversion at the Papal court.
 Lithuania, together with its new powerful ally Poland, defeated the Order in the decisive Battle of Grunwald in 1410, which is often cited as the end of the Lithuanian Crusade.
 The final peace was reached by the Treaty of Melno (1422).
The Grand Duchy of Lithuania was a European state from the 13th century until 1795.
 The state was founded by the Lithuanians, one of the polytheistic Baltic tribes from Aukštaitija.