Concerning Montgomery and "Market Garden":
Market Garden was a gamble. The idea was to get the bridges over the Maas, the Waal and the Nederrijn to get access to the Northern German plain, to encircle and cut off the Ruhr area with it´s heavy industry and maybe reach Berlin before Stalin to get a better bargaining position in the post war talks between the western allies and the Russians. At the same time it was hoped to shorten the war by a few months.
It was planned to be a combined operation of the British 2nd Army, coming up from the Belgian border through a narrow corridor in German occupied Netherlands, together with airborne assaults on the cities of Eindhoven, Veghel, Son (American 101. Airborne Division); Nijmegen, Grave (American 82nd Airborne) and Arnhem (British 1st Airborne Division and the Polish Independend Parachute Brigade).
There were several problems at Arnhem, the last and farthest bridge:
1) The drop zones were about 8 to 9 miles away from the objective. The RAF refused a closer drop to the bridge, because they claimed that a lot of AA
artillery was based around Arnhem town.
2) Due to a lack of planes, the RAF could only provide two drops a day.
The first two drops were on time, but later supply drops were delayed due to bad weather.
3) The narrow corridor through German held territory. The road was in places too soft to carry heavy equipment, and in many places it was under German artillery fire. This delayed the arrival of the British 2nd Army, which was supposed to relieve the airborne soldiers in Arnhem.
The biggest problemn was that the British and Polish airborne soldiers landed right in the middle of two SS
armoured divisions, which have been posted there a short while before for rest and training. Also this region of the Netherlands was very Nazi friendly, with many collabotators, including a school for Dutch SS
The Dutch resistance tried to warn the British military about the presence of those SS
units, but after the experiences of the "Englandspiel" (The German military intelligence Abwehr succeded through the capture of a few key SOE ansd resistance radio operators to control almost the whole resistance network and to feed false information to their British controllers, aided by easily breakable codes, they forced the radio operators for almost one year to send false messages to the British SOE. Read "Between Silk and Cyanide" by Leo Marks)
Information from the Dutch resistance wasn´t trusted anymore after the whole plot has been discovered.
The airborne managed to capture the bridge intact, but had to withdraw from it after a few days of fighting. Finaly the British and Polish Airborne got surounded at Oosterbeeck. When the 2nd Army finaly arrived, it couldn´t help them anymore, except by covering their retreat across the Nederrijn.