Spain, 1936–39
The first armed action by the Kriegsmarine was its intervention in the Spanish Civil War (17 July 1936–1 Apr 1939), in support of the Nationalist Gen Francisco Franco’s forces against those of the Spanish Republic. In Nov 1936 the German Navy sent a first 13-man advisory group; the subsequent North Sea Group (Gruppe Nordsee), with 34 instructors, remained with the Nationalist Navy until Mar 1939. A total of 35 German warships were also rotated on missions in the Atlantic Ocean and Mediterranean Sea: 3 ‘pocket battleships’ (superheavy cruisers), 6 light cruisers, the 2nd Torpedo-Boat Flotilla (12 boats), and 14 submarines. Their patrols ostensibly enforced the League of Nations nonintervention agreement, but in reality supported Franco.

Surface operations, 1939–41
On 27 Jan 1939 Hitler ordered the expansion of the Navy under Plan Z, to comprise new battleships, heavy cruisers and aircraft carriers. Unsurprisingly, only minimal work had been achieved by the outbreak of World War II on 1 Sept 1939, and in practice priority was given to expanding Admiral Dönitz’s submarine fleet. The ‘battle of Westerplatte’ in Danzig harbour (now Gdańsk, Poland) on the first day of World War II saw the old pre-World War I ship-of-the-line Schleswig Holstein shelling the Polish Army garrison.

Generaladmiral Raeder, the naval Commanderin- Chief, identified Britain’s large Royal Navy as his principal enemy. On 13 Dec 1939 in the Western Atlantic, an RN squadron forced the damaged commerce-raiding ‘pocket battleship’ Admiral Graf Spee, commanded by Kapitän zur See Hans Langsdorff, to take shelter in Montevideo on the River Plate estuary between neutral Argentina and Uruguay. Rather than risk renewing the battle against a reportedly reinforced enemy, Langsdorff scuttled Graf Spee and committed suicide. The outcome of this Battle of the River Plate, the first major naval encounter of World War II, was a welcome encouragement for the Allies. German and British submarines and destroyers undertook operations on both sides of the North Sea during Jan and Feb 1940.

From 27 Jan 1940 the Germans planned an invasion of neutral Norway to secure strategic Swedish iron ore supplies passing through Narvik. On 16 Feb an RN destroyer crew provocatively boarded the German supply ship Altmark in Norwegian waters to free prisoners taken earlier from merchantmen by Graf Spee, and Hitler ordered the planned invasion to go ahead. This formed part of Operation ‘Weserübung’ (which also violated a non-aggression pact with Denmark), and involved a dangerous North Sea crossing – the largest German amphibious operation of World War II. From 7 Apr 1940 six naval groups (Gruppen I–VI) transported German Army units to separate landing sites, evading RN Home Fleet elements which were distracted by hunting for the German capital ships. On 9 Apr the cruiser Blücher was sunk in Oslofjord by the Norwegian coastal battery at Drøbak Sound; the RN and its Fleet Air Arm then defeated the German Navy in two battles on 10 and 13 Apr, sinking several destroyers and the cruiser Königsberg (the first major warship ever to be sunk by aircraft). British, French and Free Polish troops landing from 14 Apr had some initial success in ground fighting around Narvik, but were quite outclassed by the smaller German Army landing force with its Luftwaffe support. On 8 June the Allied troops were forced to evacuate to Britain and to France, where the  German Blitzkrieg campaign had opened on 10 May. On 10 June Norway surrendered after 62 days’ resistance, but the German Navy, which had lost ten destroyers and three cruisers, regarded the Norwegian campaign as a defeat.

German naval participation in the battle of France was limited due to the superior strength of Allied warships in the English Channel, culminating in the British evacuation from Dunkirk in May–June 1940. Hitler planned an invasion of Britain (Operation ‘Seelöwe’) for Sept 1940, but Raeder was pessimistic about facing the RN in the Channel, and the Luftwaffe’s failure to defeat the Royal Air Force in the Battle of Britain (10 July–31 Oct 1940) forced a permanent postponement of this always controversial plan. Germany gained a numerically strong but unreliable ally on 10 June 1940, when Mussolini’s Fascist Italy opportunistically declared war on Britain and France. The German occupation of Norway, Denmark, the Netherlands, Belgium, and especially France in June 1940 allowed the German Navy thereafter to deploy destroyers, torpedo-boats, submarines and the formidable battleships Bismarck and Tirpitz from French ports, to threaten the RN and British merchant shipping in the Channel and the North Atlantic as well as the North Sea.

In the Atlantic, on 24 May 1941 the battleship HMS Hood was sunk by Bismarck and Prinz Eugen, followed by the engagement of an RN task force which defeated and forced the scuttling of Bismarck on 27 May. This proved that even the most powerful German warships were potentially vulnerable to combined naval and air attacks on the high seas, prompting Raeder to protect most of his operational strength at anchor in home waters and the captured harbours of western France.

In Feb 1941 the Kriegsmarine initiated its Mediterranean campaign in support of Italy, attacking Allied supply shipping to North Africa supported by the Luftwaffe; this campaign was extended in April 1941 to the Adriatic and Aegean Seas, and, from Germany’s invasion of the USSR on 21 June 1941, into the Black Sea. The most costly, though ultimately successful Allied convoys were those to re-supply the besieged island of Malta, a base for British submarines and aircraft, during 27 June 1940–31 Dec 1943. Germany made extensive use of its torpedo-boats in this theatre, in concert with successful Italian special attack units. The Russian Front was primarily a land war, but the German and Finnish navies operated in the Baltic Sea and the Kriegsmarine to a lesser extent in the Black Sea.

You can read more in The German Navy 1935–45: The Kriegsmarine in World War II