The seven dispensations in order are:
1. Innocency (Adam and Eve)
2. Conscience
3. Human Government (Gen. 9:6), beginning with Noah
4. Patriarchal Rule (Abraham, etc.)
5. Law
6. Church Age (Age of Grace)
7. Millennial Reign of Christ
I gave you a summary in ONE post.
A dispensation is an administration period paralleled by a spiritual condition not always discreet periods, there's overlap, animal sacrifices needed until Calvary -
e.g.
Eden - innocence ending with disobedience;
Antediluvian - grace or condemnation, ending with the flood, but obviously grace or condemnation continues;
Babel anarchy - continuing for mankind until Pentecost, & in a sense continuing until Jesus returns;
Grace - Covenant with Abraham & his seed, continuing throughout time;
Mosaic - Covenant of blessed relationship with God conditional on obedience, with various Messianic types provided for salvation of those who have a living faith;
Messianic - New Covenant in the blood of Jesus for all nations, ending all OC types, temple, priesthood, nation of Israel, ending with Jesus' return in glory;
NH&NE - all godless angels, spirits, people eternally condemned, all the redeemed with God in glory in his perfect Kingdom.
The redeemed are only ever saved by grace, through faith in Christ to the glory of God, throughout all dispensations.
After the fall, no-one could be saved by obedience, good works, law keeping etc.
Only Christ, as our Covenant Surety kept every detail of the Law as man for man - the second Adam.