Interestingly, there was no KPD (Communist Party of Germany) anymore in either West or East Germany after 1956.

The East German Communist Party was merged with the Social Democratic Party into the SED (Socialist Unity Party) under Soviet orders. The West German Communist Party was banned by the Constitutional Court in 1956 (some former members founded largely irrelevant splinter parties a decade later).

That of course doesn't mean that there was no far left activity in West Germany, quite the opposite to be true. In the late 60's the world wide protest movement also had a massive effect in Germany, led by far left student groups.

Widely regarded as the starting point of this time of upheaval is the visit of the Shah of Iran in 1967. In the course of a demonstration against this visit, groups of payed thugs in collaboration with the West Berlin police force beat up hundreds of protestors. One protestor was shot dead by a police officer (later revealed to be an informant for the Stasi). The official tactic of the police was to squeeze protestors together and create a mass panic. Before and after the demonstration, Germany's most widely circulated newspapers (first and foremost the tabloid BILD) kept on demonizing and insulting the protesters who in turn responded with demonstrations and protests against the yellow press.

During this time, a grand coalition of CDU/CSU and SPD was in power in West Germany. This coalition had a wide enough majority in parliament to institute constitutional changes. This further influenced the protest movement, especially the governments decision to pass a law establishing the possibility to enact emergency laws in times of unrest or war. Since similar laws during the Weimar Republic made the Nazis rise to power that much easier, it fueled the wide held belief that the political and economic elite of the Federal Republic was still massively influenced by former Nazis and in danger of being overturned.

Because the grand coalition had basically no parliamentary opposition, the self-conception of the protest movement was that they were the extraparliamentary opposition to the government.

The 68er protest movement was first and foremost a generational protest movement, largely driven by the first generation of Germans born at the end or after WW2. One of their main points of contention with the Status Quo was that the Nazi regime was kept under wraps and that no real workup of German responsibility for their crimes was happening.

On top of that the international conflicts of the time influenced them. Opposition to the Vietnam War led to massive criticism of perceived imperialist US policy and in the end a wide held Anti-Americanism in student circles.

There was no unified ideological theory behind all of the groups involved. From Marxism, to Socialism, to Maoism, to Trotskyism, the first autonomists and maybe most importantly the Frankfurt School, it was an amalgam of constantly changing political influences and schools of thought in search for what they were for but in absolute agreement what they were against. Out of this the "New Left" was born, largely in opposition to the "Old Left" (established socialist and social democratic parties (SPD) but also socialist regimes like the Soviet Union.

Some groups continued radicalizing themselves, convinced that changing the proto-fascist status quo of the Federal Republic required more direct opposition. That's when terror groups like the Red Army Faction entered the scene (early on commonly referred to as the Baader-Meinhof Gang). This group was largely influenced by South American city guerilla groups. Their terror campaign culminated in 1977, the German autumn. Their campaign to wake up the German public by exposing the government as overreaching fascists in their reaction to RAF attacks was a failure.

RAF collaboration with radical Palestinian groups like the Fatah highlighted the inherent anti-semitism of many far left groups that guised itself in anti-imperialism during this time. This further split the New Left, culminating in the modern day schism of Anti-Imperialists and Anti-Germans.

From the 80's onward it was autonomists that signified far-left opposition in West Germany. These groups worked in conjunction with the widely popular environmentalist and peace movements during the decade (environmental pollution, Chernobyl and nuclear rearmament in West Germany). In this context they saw themselves as the militant wing of public opposition to these topics, mostly involved in street fighting. They also started a big squatting movement in Germany and especially West Berlin where hundreds of houses were crumbling and empty while rents throughout were rising. It didn't look much different in East Berlin and when the wall came down they took over a whole street in Berlin-Friedrichshain, the Mainzer Straße, and held it for seven months before the police stormed the barricades with massive force in what looked like a battle of the French Revolution.