The nine-man court in the weeks and months ahead will tackle a heavy docket of cases studded with problems of racial integration in public schools. It will also consider applications of the Smith Act, the government's primary weapon against the Communist party.

The opening session way by tradition, held to brief formalities. Next Monday the court will begin hearing arguments on the renewed attacks against the Smith Act. The court will determine late this month what action, if any, it will take in the school segregation cases.

166th Year

The court's 166th year opened at noon when Chief Justice Earl Warren led his eight black-robed colleagues into the high-ceilinged, marble-column chamber.

The 26 - minute session ended with the admission of 83 attorneys to practice before the court.

For Associate Justice Sherman Minton, this week and next will be his last on the high bench. Minton, 65, is retiring Oct. 15 because of ill health.

President Eisenhower Saturday named William J. Brennan Jr., of New Jersey to succeed him. Brennan's appointment is subject to approval of the Senate.

Probably no other matter on the court's docket will receive the attention certain to be given the court's actions in school segregation cases.

Summer Recess

During the summer recess three appeals were filed from District Court cases stemming from the high court's order last year to end enforced segregation in public schools "with all deliberate speed."

Many more cases on the same issue are expected during the present nine-month term.

In its 1955 order the court said U.S. District Courts, because of their knowledge of local circumstances, could best see to it that school boards made "a prompt and reasonable" start toward ending segregation.

The court's handling of appeals involving District Court decisions will indicate how closely it intends to supervise the carrying out of its 1955 order.