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A
 1, 2, 3, 4, 5, 6, 7, 8, 9
B
 1, 2, 3, 4, 5, 6, 7, 8, 9
C
 1, 2, 3, 4, 5, 6, 7, 8, 9
D
 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9
E
 1, 2, 3, 4, 5, 6, 7, 8, 9
F
 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9
G
 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9
H
 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

A preview for volume 2

Volume 2 of the Crossnumber Book contains a description of how this puzzle was created.
Across:
A: A square number.
C: If one adds the average value of E across's digits to C across, the result equals B down divided by C across.
E: A cubic number.
G: A palindrome whose digit sum equals F down.
H: A square number.
Down:
A: Half of the reverse of H across.
B: G across minus C down.
C: All digits are the same.
D: To get D down, add F down's digit product and F-down's digit sum and multiply the result with F down.
F: This cubic number equals the digit sum of B down.