The Battle of Arnhem was the British 1st Airborne Division's contribution to Operation Market Garden. This was Montgomery's plan to sieze the major river and canal bridges, all the way to the Rhein, with airborne forces and break through to them in a rapid advance from the British 30th Corps.
The operation didn't go to plan for many reasons and 1st Airborne Division and the Polish Airborne Brigade with them, were badly mauled by Elite German SS forces, that weren't expected to be in the area, and only a few thousand of the 10 thousand strong division was extracted over the river during darkeness ten days after they landed.
Often pointed to by members of the Intelligence Corps as an example of what not listening to your G2 staff leads to, ie a glorious failure. The German forces onto which the Paras were dropped were identified weeks before the battle. The Int Corps Major in charge tried to point this out to his superiors but got sent home for his pains.
The Battle of Arnhem was depicted in the exelent 1970s film "A Bridge Too Far", but anyone who really wants to see the ultimate 'Arnhem' film has to see "Theirs is the Glory" which is filmed in black and white, on location and by soldiers who were there during the battle. "A Bridge Too Far" was not shot in Arnhem at all. The area where the battle was fought between a full division of Para's and two full of SS did not survive. (The only thing of beauty to come out of there was Audrey Hepburn!). The movie was shot downstream of the IJssel river in Zutphen and Deventer. The bridge seen in the film is the one in Deventer, but the buildings close to it are props. One German HQ is the old Town Hall of Zutphen and another is the one in Deventer. I can go on about this, but I won't it'll make me look like the anorak I deep down am...