1 - In the last six months I have been to London 3 times. (things I have done during this period of time) 2 - For the last six months I have been learning a new language (things I have been doing over this period of time 3 - In the past six months - (same as no. 1) 4 - For the past six months - (same as no. 2) 5 - last month (finished time period) 6 - past month (period of time - up to now) (include today or not?) - For 1,2,3,4,6: yes: up to the moment of speaking/ writing - up to the present moment... No. 5 is finished past time - not including today. Is it a period? - Yes - 6 months/ 1 month in your examples. past or not? - All of your examples refer to the past. I hope that answers your questions...