Battle of Grunwald
To keep their plans secret and mislead the order, Władysław II Jagiełło and Vytautas organized several raids into border territories, thus forcing the order to keep their troops in place.

Opposing forces: The precise number of soldiers involved has proven difficult to establish. None of the contemporary sources provided reliable troop counts. Jan Długosz provided the number of banners, the principal unit of each cavalry: 51 for the Teutons, 50 for the Poles and 40 for the Lithuanians. However, it is unclear how many men were under each banner. The structure and number of infantry units (pikemen, archers, crossbowmen) and artillery units is unknown. Estimates, often biased by political and nationalistic considerations, were produced by various historians. German historians tend to present lower numbers, while Polish historians tend to use higher estimates. The high-end estimates by Polish historian Stefan Kuczyński of 39,000 Polish–Lithuanian and 27,000 Teutonic men have been cited in Western literature as "commonly accepted".
While outnumbered, the Teutonic army had advantages in discipline, military training and equipment. They were particularly noted for their heavy cavalry, although only a small percentage of the Order's army at Grunwald were heavily armoured knights. The Teutonic army was also equipped with bombards that could shoot lead and stone projectiles.
Both armies were composed of troops from several states and lands, including numerous mercenaries, primarily from Silesia and Bohemia. Bohemian mercenaries fought on both sides. The Silesian mercenaries were led in battle by Duke Konrad VII the White, of Oels, who was supported by knights from the Silesian nobility including Dietrich von Kottulin and Hans von Motschelnitz. 
Soldiers from twenty-two different states and regions, mostly Germanic, joined the Order's army. Teutonic recruits known as guest crusaders included soldiers from Westphalia, Frisia, Austria, Swabia, Bavaria, and Stettin (Szczecin). Two Hungarian nobles, Nicholas II Garai and Stibor of Stiboricz, brought 200 men for the Order, but support from Sigismund of Hungary was disappointing.
Poland brought mercenaries from Moravia and Bohemia. The Czechs produced two full banners, under the command of John Sokol of Lamberg. Serving among the Czechs was possibly Jan Žižka, future commander of the Hussites. Alexander I of Moldavia commanded an expeditionary corps and the Moldavian king was so brave that the Polish troops and their king honoured him with a royal sword, the Szczerbiec. Vytautas gathered troops from Lithuanian and Ruthenian lands (present-day Belarus and Ukraine). Among them were three banners from Smolensk led by Władysław II Jagiełło's brother Lengvenis, the Tatar contingent of the Golden Horde under the command of the future Khan Jalal al-Din, and Armenian cavalry troops from Podolia. The overall commander of the joint Polish–Lithuanian force was King Władysław II Jagiełło; however, he did not directly participate in the battle. The Lithuanian units were commanded directly by Grand Duke Vytautas, who was second in command, and helped design the grand strategy of the campaign. Vytautas actively participated in the battle, managing both Lithuanian and Polish units. Jan Długosz stated that the low-ranking swordbearer of the Crown, Zyndram of Maszkowice, commanded the Polish army, but that is highly doubtful. More likely, marshal of the Crown Zbigniew of Brzezia commanded the Polish troops in the field.

Course of the battle: 

March into Prussia: The first stage of the Grunwald campaign was the gathering of all Polish–Lithuanian troops at Czerwińsk, a designated meeting point about 80 km (50 mi) from the Prussian border, where the joint army crossed the Vistula over a pontoon bridge. This maneuver, which required precision and intense coordination among multi-ethnic forces, was accomplished in about a week, from 24 to 30 June. Polish soldiers from Greater Poland gathered in Poznań, and those from Lesser Poland, in Wolbórz. On 24 June, Władysław II Jagiełło and Czech mercenaries arrived in Wolbórz. Three days later the Polish army was already at the meeting place. The Lithuanian army marched out from Vilnius on 3 June and joined the Ruthenian regiments in Hrodna. They arrived in Czerwińsk on the same day the Poles crossed the river. After the crossing, Masovian troops under Siemowit IV and Janusz I joined the Polish–Lithuanian army. The massive force began its march north towards Marienburg (Malbork), capital of Prussia, on 3 July. The Prussian border was crossed on 9 July.
The river crossing remained secret until Hungarian envoys, who were attempting to negotiate a peace, informed the Grand Master. As soon as Ulrich von Jungingen grasped the Polish–Lithuanian intentions, he left 3,000 men at Schwetz (Świecie) under Heinrich von Plauen and marched the main force to organize a line of defense on the Drewenz River (Drwęca) near Kauernik (Kurzętnik). The river crossing was fortified with stockades. On 11 July, after meeting with his eight-member war council, Władysław II Jagiełło decided against crossing the river at such a strong, defensible position. The army would instead bypass the river crossing by turning east, towards its sources, where no other major rivers separated his army from Marienburg. The march continued east towards Soldau (Działdowo), although no attempt was made to capture the town. The Teutonic army followed the Drewenz River north, crossed it near Löbau (Lubawa) and then moved east in parallel with the Polish–Lithuanian army. According to the Order's propaganda, the latter ravaged the village of Gilgenburg (Dąbrówno). Later, in the self-serving testimonies of the survivors before the Pope, the order claimed that Von Jungingen was so enraged by the alleged atrocities that he swore to defeat the invaders in battle.

Battle preparations: In the early morning of 15 July, both armies met in an area covering approximately 4 km2 (1.5 sq mi) between the villages of Grunwald, Tannenberg (Stębark) and Ludwigsdorf (Łodwigowo). The armies formed opposing lines along a northeast–southwest axis. The Polish–Lithuanian army was positioned in front and east of Ludwigsdorf and Tannenberg. Polish heavy cavalry formed the left flank, Lithuanian light cavalry the right flank and various mercenary troops made up the center. Their men were organized in three lines of wedge-shaped formations about 20 men deep. The Teutonic forces concentrated their elite heavy cavalry, commanded by Grand Marshal Frederic von Wallenrode, against the Lithuanians. The order, which was the first to organize their army for the battle, hoped to provoke the Poles or Lithuanians into attacking first. Their troops, wearing heavy armor, had to stand in the scorching sun for several hours waiting for an attack. One chronicle suggested that they had dug pits that an attacking army would fall into. They also attempted to use field artillery, but a light rain dampened their powder and only two cannon shots were fired. As Władysław II Jagiełło delayed, the Grand Master sent messengers with two swords to "assist Władysław II Jagiełło and Vytautas in battle". The swords were meant as an insult and a provocation. Known as the "Grunwald Swords", they became one of the national symbols of Poland.

Battle begins: Lithuanian attack and retreat maneuver: Vytautas, supported by the Polish banners, started an assault on the left flank of the Teutonic forces. After more than an hour of heavy fighting, the Lithuanian light cavalry began a full retreat. Jan Długosz described this development as a complete annihilation of the entire Lithuanian army. According to Długosz, the Order assumed that victory was theirs, broke their formation for a disorganized pursuit of the retreating Lithuanians, and gathered much loot before returning to the battlefield to face the Polish troops. He made no mention of the Lithuanians, who later returned to the battlefield. Thus Długosz portrayed the battle as a single-handed Polish victory. This view contradicted Cronica conflictus and has been challenged by modern historians.
Starting with an article by Vaclaw Lastowski in 1909, they proposed that the retreat had been a planned maneuver borrowed from the Golden Horde. A feigned retreat had been used in the Battle of the Vorskla River (1399), when the Lithuanian army had been dealt a crushing defeat and Vytautas himself had barely escaped alive. This theory gained wider acceptance after the discovery and publication, in 1963 by Swedish historian Sven Ekdahl, of a German letter.