Months of the Year

January.
This month was named after the Roman god Janus. Who had two faces, one looking back and the other looking forward. Fitting for the first month of the year.

February.
This month was named forfebrua meaning month of purification and offerings.

March.
This month was named after the Roman god of war Mars.

September
When the Romans introduced the Julian calendar, they retained several month names from their old Roman calendar, despite the fact that these months no longer had the same position on the calendar. Thus, September, once the Roman seventh month of the year, deriving from the Latin septem, " seven", remained as the ninth month of the year.
QPB Encyclopedia of Word and Phrase Origins By Robert Hendrickson

October

Latin, the ninth month of the primitive Roman calendar, which began in March, fr. octo eight: cf.F. Octobre.

1. The tenth month of the year, containing thirty-one days.
2. Ale or cider made in that month.

   The country gentlemen had a posset or drink they called October.
   --Emerson.

Webster's Revised Unabridged Dictionary (1913)

November

The Ninth moth. The ancient Romans calculated the begining of their year in March. Hence they named the ninth month novembris or november. November and Novembris were derivatives of latin novem "nine."

Source: Dictionary of Word Origins by John Ayto

December.
This month is named after the Roman word Deca meaning 10. In the original Roman calendar there were only 10 months.