(John 17:1-3) These words spake Jesus, and lifted up his eyes to heaven, and said, Father, the hour is come[of my crucifixion on the cross, to pay the penalty for (our) sin]; glorify thy Son, that thy Son also may glorify thee: As thou hast given him power[authority (delegated authority)] over all flesh, that he should giveeternal life to as many asthou hast given him [i.e. not to everybody in the world]. And this islife eternal, that they might know thee[be aware of, have knowledge of, perceive, understand] the only true God, and Jesus Christ, whom thou hast sent.
(John 1:29) The next day John seeth Jesus coming unto him, and saith, Behold the Lamb of God, which taketh away the sin of the world[kosmos; “cosmos” orderly arrangement].
cosmos = Dict: 1. the world or universe as an embodiment of order and harmony (as distinguished from chaos). 2. a complete and harmonious system. 3. order; harmony.
The Full Life Study Bible (with some changes): Eternal life is more than endless existence. It is a special quality of life that we as believers receive when we partake of the life of God through Christ; this allows us to know God in an ever-growing knowledge, and fellowship with the Father, Son, and Holy Spirit. In the New Testament eternal life is described as: