Augustine On Fallen Human Nature

This is taken from one of my theology textbooks. Read the words carefully because there is a lot there in so few words:
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In this important discussion of fallen human nature, originally written in Latin in 415, Augustine identifies the consequences of the Fall upon human nature. Originally created without any fault, human nature is now contaminated by sin, and can only be redeemed through grace.

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Human nature was certainly originally created blameless and without any fault [vitium]; but the human nature by which each one of us is now born of Adam requires a physician, because it is not healthy. All the good things, which it has by its conception, life, senses, and mind, it has from God, its creator and maker. But the weakness which darkens and disables these good natural qualities, as a result of which that nature needs enlightenment and healing, did not come from the blameless maker but from original sin [ex originali peccato], which was committed by free will [liberum arbitrium].

For this reason our guilty nature is liable to a just penalty. For if we are now a new creature in Christ, we were still children of wrath by nature, like everyone else. But God, who is rich in mercy, on account of the great love with which He loved us, even when we were dead through our sins, raised us up to life with Christ, by whose grace we are saved. But this grace of Christ, without which neither infants nor grown persons can be saved, is not bestowed as a reward for merits, but is given freely [gratis], which is why it is called grace [gracia]. [...]

For this reason it is that those who are not made free by that blood (whether because they have not been able to hear, or because they were not willing to obey, or were not able to hear on account of their youth, and have not received the bath of regeneration which they might have done and through which they might have been saved) who are mostly justly condemned because they are not without sin, whether they derived from their origins or were acquired by evil actions. For all have sinned, whether in Adam or in themselves, and have fallen short of the glory of God (Romans 3:23).

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Notice the Latin terms gratis (freely or without cost) and gratia (grace or gift). Do you see a connection? What is grace?