General Montgomery's plan to capture bridges across the rivers and canals in Holland that would allow the Allied advance to continue into northern Germany, unimpeded by these natural defensive lines. German forces in Holland and especially in the Arnhem area are much stronger than anticipated. The plan proved too ambitious.
The execution of Operation Market Garden proceeded successfully at first, however, the relative strength of the German armed forces in the line of advance slowed progress. Nonetheless, in the period, Allied armed forces reached the German border, releasing all of France and Belgium from Nazi occupation.
Although generally acknowledged to be unrealistic, the German military intention in attacking through the Ardennes Forest to Antwerp was to cut off the northern Allied armies. The last reserves of German armored forces were secretly built up for that purpose in the area.
German armed forces achieved strategic surprise in launching the offensive. The relatively weak American military forces blocking their advance managed to slow down the German troops sufficiently to all for an American regrouping which then effectively prevented further progress. The advantage of Allied air superiority was initially hampered by poor weather.
Following on the defeat of the German Ardennes offensive, Allied armed forces broke through towards the Rhine within the German frontier. Crossing the Rhine became the next major objective.
American armed forces achieved tactical surprise at Remagen and captured the railway bridge. The first Allied bridgehead across the Rhine was thus established.
The fight for the Ludendorff Bridge across the Rhine was intensive and day-long. The bridge was weakened during the fighting and eventually collapsed. By then, a firm American bridgehead had already been established.
In the weeks following the bridge at Remagen, several other bridgeheads were established over the Rhine and these were also quickly built-up.
Rhine crossings were also established north of the Ruhr industrial area of Germany. These served as the northern pincer of the envelopment of the Ruhr and the consequent encirclement of German Army Group B.
With the Rhine River obstacle overcome, Allied armed forces began a final drive which encircled Army Group B in the Ruhr valley and pressed eastward toward the Elbe River -- the agreed upon demarcation of Allied and Soviet forces advancing from west and east respectively. American military forces in the south exploited southeast into Austria and Czechoslovakia after achieving this objective.