Acts 1:3,4 - After His suffering

1:3

“After His suffering ...” refers, of course, to the cross. Perhaps Luke is also alluding to the suffering that the apostles themselves would soon have to endure. However, the key point here is that Jesus demonstrated to them that He really was alive. He appeared to them over a period of forty days, and spoke about the kingdom of God. When Jesus started His ministry went around teaching that the kingdom of God was near. We can have no proper concept of the kingdom of God unless we see Jesus at the centre of it all.

1:4

“While He was eating with them” is a throwaway remark, but emphasises the reality of the resurrection. Jesus was different after the resurrection, but still had a physical body. The disciples were told not to leave Jerusalem until they had received  the Holy Spirit. The book of Acts makes no sense without the Holy Spirit. “The gift my Father promised” refers back to verse like Joel 2:28-32.