What were the German advances in the west in 1914-1918?
You have tagged this with "trench warfare," and the fact that trench warfare dominated this time period shows us that there were very few German advances in the west after the very beginning of the war.
At the beginning of the war in 1914, Germany was able to advance quickly. It through Belgium and deep into France, coming very close to Paris before it was stopped at the Battle of the Marne in September of that year. After that, there was no real further movement until 1918. At that point, the Germans used a new tactic that relied more on surprise than on huge artillery barrages and mass attacks. They were trying to achieve victory before the American forces arrived in France and helped to turn the tide. This "Spring Offensive" allowed them to move forward almost 40 miles, but it was not able to completely break down French and British resistance.