Forced to abandon his plans to invade Britain Napoleon turned his Grande Armee east to deal with the threat of an Austrian-Russian Allied army. Not so much of a battle but a series of concentric manoeuvres in the vicinity of Ulm would lead to the capitulation of an Austria Army and would leave the way open for Napoleon's victory at Austerlitz on 2nd December 1805.
Napoleon realized that he had to defeat the Austrian General Mack von Leiberich, before going on to face the rest of the Austrian Army and their Russian allies. Keeping the Manoeuvre of Ulm a secret as long possible by getting his commanders to announce that they were returning to Paris, Napoleon's Grande Armee moved across the River Rhine at an unheard of pace.
By the 30th of September just eleven days after crossing the Rhine French troops were passing over the Danube and the Austrian General Mack realized that he was about to be attacked from the rear so he concentrated his army east of Ulm which sits at the confluence of the Iller and Danube rivers about 48 miles south-east of Stuttgart. The French quickly encircled the Austrians as their commanders did nothing and trapped 72,000 Austrian troops with 200,000 French troops. The Austrians lost around 50,000 killed , wounded or captured and 65 guns with only one Austrian corps making it out with Mack only for him to surrender his 27,000 remaining troops later on the 20th an act which destroyed his reputation. The French lost only around 6,000 which left Napoleon free to turn northwards towards Austerlitz here he would face an Allied army of around 300,000. On the 21st October as Mack's army marched out of Ulm into French hands Vice Admiral Lord Nelson won a victory at Trafalgar over the French-Spanish fleet guaranteeing the Royal Navy's mastery of the sea and insuring that the planned French invasion of Britain could not take place.