When the first world war began the german high command knew that they would fight a war on two fronts. They therefor planed for this inn advance and concluded that since Russia was so large it would take a long time for them to mobilize and they decided that this would give the german army enough time to destroy the french army and deal the killing blow to France before facing the russians. To do this the invasion of France had to be quick. They further concluded that since the french-german border was so well fortified they had to go through Belgium and the Netherlands(this was later changed to just Belgium). When the war began they immideatly invaded Belgium and 7 August the fortress at Liége fell to the Germans. The belgians fell back to their other fortified cities, Namur and Antwerp and three german armies(750 000 men) moved quickly after them. At the same time the french launched a large counter-offensive in Alsace-Lorraine, but they were driven back by german machine gun fire and suffered heavy casualties. The german counter-attack saw some 20 000 french captured by the germans. French attacks in the Ardenne was as disasterous and Lanrezacs armé(the french fifth army) began retreating from Namur. 23 August the BEF came into contact with the German 1st army at the Mons Conde Cannal and the germans pushed them back, but took heavy casualties. After these initial engagements the french and british decided to fall back towards Paris and regroup there. The retreat was well organised and they rarely lost large amounts of men and equipment. The germans tried to attack in the south, around Nancy, without any luck. Two german armies continued towards Paris where the french and british had reorganized and were ready to meat them. The germans moved to the east of Paris, but bad communcation between the armies ended in a hole in the line. The BEF was incidentally where this hole formed and advanced, driving a wedge between the armies. Fearing being surrounded the german 2nd army retreated and forced the 1st army to follow. They fell back towards the Aisne river where they crossed the river and dug inn with trenches and barbed wire. The french followed them but were driven back and the front ended in a stalemate as the french and british also dug in. Neither of the sides had commited men north of this position and to try to break the deadlock both sides tried to outflank the other side, but since both sides moved northwards they always met resistance and dug inn with trenches and barbed wire. The race northwards ended when they hit the channel coast. Inn the south the situation had developed similarly and the entire western front ended in a stalemate.

During this time the french army did not equip their soldiers with shovels and therefor had problems digging inn and both the french and british armies lacked as many machine guns as the germans, but the largest problem was probably that the french commanders ordered their armies to fall back. When the germans followed it hindered the french and british from properly digging inn.

Although the western front ended in a stalemate by the winter of 1914 the eastern front continued to be a war of mobility and it never ended in a stalemate. And why should it? the eastern front was enormous and there were no more men in the east than in the west.

If you have any questions i would be glad to answer and thank you very much for your patience.

Sources:https://www.worldcat.org/title/world-war-one-a-short-history/oclc/695008475&referer=brief_results

Note: I used a norwegian translation of the book, but could not find it, so i linked to the original