‘The elder to Gaius the beloved, whom I love in truth.'
The writer again calls himself ‘the Elder'. As with 2 John the impression is given that all would know who was meant. He was not just one of many elders but seen as unique. There is no real reason for denying that it is the Apostle John, who as we know from John's Gospel, preferred not to push his name forward. He was probably delighted with a term that, as used by his fellow-believers, indicated warm affection as well as respect.
Gaius, to whom the letter is addressed, is a man of the truth, and John loves him truly because he is of the truth. He is indeed ‘beloved by' John. Gaius is ‘loved in truth'. This can mean truly loved, or loved as one who is of the truth. Or perhaps John intended it to have the double meaning. A man of true faith loved in truth. Certainly the implication of both is there.