The Indwelling or Abiding of the Holy Spirit in the believer.

The Holy Spirit indwells the believing sinner.

Joh 14:20  Jesus said, "At that time you will know that I am in my Father, and that you are in me, and that I am in you".

At that day ye shall know,.... The things they should know, or the objects of knowledge are,

that I am in my Father; in his bosom, in union with him, partaker of the same nature, perfections, and glory with him, and equal to him:

and you in me: that they were in union with him as the branches in the vine, and as the members are in the head, and how they were loved in him, chosen in him, righteous in him, risen with him, and made to sit together in heavenly places in him:

and I in you; formed in their hearts, living in them, dwelling in them, as in His temples, and filling them with grace and glory. The knowledge of these things promised, designs a more clear and distinct knowledge of them; something of them was known already, but not so perfectly as should be hereafter; and this does not suppose that these unions between the Father and Christ, and between Christ and his people, shall then begin to be; for as the union between the Father and the Son is as eternal as themselves; so the union between Christ and his people, as he is the head and representative of them, is as early as his investiture with the office of a Mediator, and his suretyship engagements for them, which were from eternity; J. Gill

1Co 2:12  But we have not received the spirit of the world, but the Spirit which comes forth from God, that we may know the blessings that have been so freely given to us by God.

Not the spirit of the world (ou to pneuma tou kosmou). Probably a reference to the wisdom of this age in 1Co_2:6. See also Rom_8:4, Rom_8:6, Rom_8:7; 1Co_11:4 (the pneuma heteron).

But the Spirit which is of God (alla to pneuma to ek theou). Rather, “from God” (ek), which proceeds from God.

That we might know (hina eidōmen). Second perfect subjunctive with hina to express purpose. Here is a distinct claim of the Holy Spirit for understanding (Illumination) the Revelation received. It is not a senseless rhapsody or secret mystery, but God expects us to understand “the things that are freely given us by God” (ta hupo tou theou charisthenta hēmin). First aorist passive neuter plural articular participle of charizomai, to bestow. God gave the revelation through the Holy Spirit and he gives us the illumination of the Holy Spirit to understand the mind of the Spirit.

The tragic failures of men to understand clearly God’s revealed will is but a commentary on the weakness and limitation of the human intellect even when enlightened by the Holy Spirit. RWP

1Co 3:16  Do you not know that you are God's Sanctuary, and that the Spirit of God has His home within you?

1Co 3:17  If any one is marring the Sanctuary of God, him will God mar; for the Sanctuary of God is holy, which you all are.

1Co 3:18  Let no one deceive himself. If any man imagines that he is wise, compared with the rest of you, with the wisdom of the present age, let him become "foolish" so that he may be wise.

v.16 Know ye not — It is no new thing I tell you, in calling you “God’s building”; ye know and ought to remember, ye are the noblest kind of building, “the temple of God.”

ye — all Christians form together one vast temple. The expression is not, “ye are temples,” but “ye are the temple” collectively, and “lively stones” (1Pe_2:5) individually.

God’s ... Spirit — God’s indwelling, and that of the Holy Spirit, are one; therefore the Holy Spirit is God. No literal “temple” is recognized by the New Testament in the Christian Church. The only one is the spiritual temple, the whole body of believing worshippers in which the Holy Spirit dwells (1Co_6:19; Joh_4:23, Joh_4:24). The synagogue, not the temple, was the model of the Christian house of worship. The temple was the house of sacrifice, rather than of prayer. Prayers in the temple were silent and individual (Luk_1:10; )

Joh 14:16  And I will ask the Father, and He will give you another Advocate to be for ever with you-- Spirit of truth.

Barnes Notes: Another Advocate - Comforter - Jesus had been to them a counsellor, a guide, a friend, while he was with them. He had instructed them, had borne with their prejudices and ignorance, and had administered consolation to them in the times of despondency. But he was about to leave them now to go alone into an unfriendly world. The other Comforter was to be given as a compensation for his absence, or to perform the offices toward them which he would have done if he had remained personally with them. And from this we may learn, in part, what is the office of the Spirit. It is to furnish to all Christians the instruction and consolation which would be given by the personal presence of Jesus, Joh_16:14. To the apostles it was particularly to inspire them with the knowledge of all truth, Joh_14:26; Joh_15:26. Besides this, he came to convince men of sin. See the notes at Joh_16:8-11. It was proper that such an agent should be sent into the world:

1. Because it was a part of the plan that Jesus should ascend to heaven after his death.

2. Unless some heavenly agent should be sent to carry forward the work of salvation, man would reject it and perish.

3. Jesus could not be personally and bodily present in all places with the vast multitudes who should believe on him. The Holy Spirit is omnipresent, and can reach them all. See the notes at Joh_16:7.

4. It was manifestly a part of the plan of redemption that each of the persons of the Trinity should perform His appropriate work the Father in sending His Son, the Son in making atonement and interceding, and the Spirit in applying the work to the hearts of men.

The word translated “Comforter” is used in the New Testament five times. In four instances it is applied to the Holy Spirit - Joh_14:16, Joh_14:26; Joh_15:26; Joh_16:7. In the other instance it is applied to the Lord Jesus - 1Jo_2:1; “We have an advocate (Paraclete - Comforter) with the Father, Jesus Christ the righteous.” It is used, therefore, only by John. The verb from which it is taken has many significations. Its proper meaning is to call one to us Act_27:20; then to call one to aid us, as an advocate in a court; then to exhort or entreat, to pray or implore, as an advocate does, and to comfort or console, by suggesting reasons or arguments for consolation. 
The word “comforter” is frequently used by Greek writers to denote an advocate in a court; one who intercedes; a monitor, a teacher, an assistant, a helper. It is somewhat difficult, therefore, to fix the precise meaning of the word. It may be translated either advocate, monitor, teacher, or helper. What the office of the Holy Spirit in this respect is, is to be learned from what we are elsewhere told he does. We learn particularly from the accounts that our Saviour gives of his work that that office was:

1. to comfort the disciples; to be with them in his absence and to supply his place; and this is properly expressed by the word Comforter.

2. to teach them, or remind them of truth; and this might be expressed by the word monitor or teacher, Joh_14:26; Joh_15:26-27.

3. to aid them in their work; to advocate their cause, or to assist them in advocating the cause of religion in the world, and in bringing sinners to repentance; and this may be expressed by the word advocate, Joh_16:7-13. It was also by the Spirit that they were enabled to stand before kings and magistrates, and boldly to speak in the name of Jesus, Mat_10:20. These seem to comprise all the meanings of the word in the New Testament, but no single word in our language expresses fully the sense of the original.

That he may abide with you for ever - Not that he should remain with you for a few years, as I have done, and then leave you, but be with you in all places to the close of your life. He shall be your constant guide and attendant. Barnes

Compare Jn 7:37-39;  1Jn 3:24; 2 Cor 5:17

Rom 8:9  You, however, are not devoted to earthly, but to spiritual things, if the Spirit of God is really dwelling in you; whereas if any man has not the Spirit of Christ, such a one does not belong to Him.

Rom 8:10  But if Christ is in you, though your body must die because of sin, yet your spirit has Life because of righteousness.

Rom 8:11  And if the Spirit of Him who raised up Jesus from the dead is dwelling in you, He who raised up Christ from the dead will give Life also to your mortal bodies because of His Spirit who dwells in you.