Work has started on the first phase of the new Senior Center near the town’s swim club on Sohier Street, and is expected to be finished by the end of this year, according to a spokesman for the project. Rick Stockwood said the 8,000-square-foot building will cost an estimated $3.5 million and includes a large multipurpose room for meals and functions, smaller activity rooms, and office space for the town’s Elder Affairs department, veterans’ agent and town nurse. The Social Service League of Cohasset has pledged $1 million for the project and is taking the lead in raising the rest of the money from individuals, businesses and foundations — bringing in an additional $900,000 so far, Stockwood said. He said a formal groundbreaking and townwide fund-raising campaign is scheduled for the end of March. Plans for a second phase of the project — added space for an elder day care facility — are on hold until the new center opens, he said. “We are excited that this new Senior Center is on its way,” Stockwood said in an interview.