The arrival of agriculture is thought to have originated in the Middle-East and propagated as a "wave" through Europe with the earliest in Greece and the latest in northern Europe.
The technological advance of agriculture allowed an increased population density from the Palaeolithic hunter gatherers.
Genetic analysis suggests that the first Principle Component represents this spread due to the date (post the last glacial maximum) and geographical distribution are strikingly similar.
The genetic evidence shows that the wave of agriculture assimilated the previous populations giving a genetic distribution across Europe with the maximum of Neolithic genes in the south east and the minimum in Scandinavia, thus outdating the "migration" theories.
This spread of agriculture is based on the arrival of wheat from the Middle-East (ref: Cavalli-Sforza).
Ceramic pottery arrived in Europe around the same time with differing regional forms.
The spread of Indo-European languages into Europe from a "homeland" either in the middle east or north of the Black Sea has been suggested to be associated the spread of agriculture.
There is much confusing speculation and arguments to justify personal theories. These frequently attempt to place Greece at the hub of European agriculture, language, and civilisation.