Napoleon had to rebuild his army following the failure of his 1812 campaign in Russia. The 1813 class of conscripts had already been called up, meaning that 137,000 men were nearing the end of their training at the start of 1813.
More men were found from the National Guard, a home defence militia, the navy and Italy. Troops were also transferred from Spain to the German front. Others were found by calling up the 1814 class of conscripts early, along with men who had managed to evade the draft for health or other reasons in earlier years.
The new army was large and would fight bravely, but many of the infantry were either young and inexperienced or else old. It was harder to replace the horses than the men lost in Russia. The lack of cavalry would prove to be a major problem for Napoleon in 1813.
The French Empire managed to replace the cannons lost in Russia, but they needed horses to pull them, as did supply wagons, creating logistical difficulties.
Napoleon also had problems with the quality of his generals. According to David Chandler, the mid-ranking officers were still good, but the marshals were tired and past their best, whilst the junior ones were inexperienced.
Whilst rebuilding his army, Napoleon left Marshal Joachim Murat in command in Germany. The Emperor had hoped that Murat would be able to hold the Russians along the River Vistula, but he was forced to retreat to Posen (now Poznan). He then handed over command to Napoleon’s step-son Prince Eugène, and returned to his kingdom of Naples.
Eugène had too few troops to fight, and the frozen rivers were no help to the defender. Despite orders from Napoleon to hold, he was forced to withdraw his forces, apart from some isolated garrisons, behind the River Elbe.
Tsar Alexander I of Russia was, according to Dominic Lieven, effectively his own foreign minister. He was with his army, whilst the official foreign minister, Nikolai Rumiantsev, was in St Petersburg. Alexander’s aim was to force France behind its natural frontiers. Rumiantsev thought that the Tsar was too focused on Napoleon, paid too little attention to the Ottoman Empire and Persia and was too keen to satisfy the Austrians and British. 
Prussia had been forced to contribute a corps to Napoleon’s invasion of Russia, but on 30 December 1812 its commander, General Ludwig Yorck, signed the Convention of Tauroggen with Russia, making his troops neutrals. He acted without the consent of King Friedrich Wilhelm III, but the news was received enthusiastically in Prussia.
Friedrich Wilhelm, according to Lieven, ‘detested Napoleon and…liked and admired Alexander…[but] was a great pessimist. He hesitated until the Russian had reached Prussia, but on 28 February 1813 Russia and Prussia signed the Treaty of Kalisz. Five days later the Russian entered Berlin.
The main sticking point in the negotiations was Poland. Friedrich Wilhelm did not want to lose any of the territory that Prussia had gained from the 18th century partitions of Poland. Alexander, however, thought that the only way to deal with Polish nationalism without weakening Russian security was to have a Polish kingdom whose monarch was the Russian Tsar. The agreement was that Prussia would be restored to its 1806 size, receiving northern German territory and population to compensate it for any losses in Poland.
The treaty required both parties to attempt to bring Austria into their alliance. The Austrians, however, were cautious for now.
On 16 March Prussia declared war on France. Napoleon had limited the size of its army to 42,000 after defeating it in 1806, but allowed it to recruit more in late 1812. The Prussians had also secretly created a reserve by forcing a proportion of their soldiers to retire each year. They were therefore able to field 80,000 well trained troops, backed by the Landwehr, a conscript militia and volunteer units.
Charles Esdaile argues that only a ‘very small number’ joined because of German nationalism, but Prussia did have 270,000 troops by the summer.
Defensive manoeuvring continued until early April. By then Eugène had withdrawn from the Elbe because the Prussians were massing near Dresden, and had deployed his troops in a strong defensive position with his right flank on the River Saale.
 D. Chandler, The Campaigns of Napoleon (London: Weidenfeld & Nicolson, 1966), p. 866.
 Ibid., p. 868.
 D. C. B. Lieven, Russia against Napoleon: The Battle for Europe, 1807 to 1814 (London: Penguin, 2010), pp. 285-90.
 Ibid., p. 293.
 C. J. Esdaile, Napoleon’s Wars: An International History, 1803-1815 (London: Allen Lane, 2007), p. 494.