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Here's my best guess at how all of this works based upon how the data is laid out. Please do correct me if there are errors! I have not played this in-game. I do not confirm any of the following to be 100% true or accurate.

There was one thing that really surprised me about all of this. Scattered throughout the WZ files, sometimes there's documentation left by the kind folks who created each piece of content (in the way of "info/" blocks). What surprised me about this was that some of the info blocks were written in Korean and the others were written in Japanese. This leads me to believe that the Koreans began coding the information and the Japanese finished what the Koreans started.

You are given a Monster Book, and you receive a certain number of points for your monster book as you collect more cards (the data makes no note of which mobs give how many points). Once you attain a certain number of points, your Monster Book levels up:

Points	All Stat
0	+1
10	+2
100	+3
300	+4
600	+5
1000	+6
2000	+7
4000	+8
7000	+9
10000	+10

It would also appear that as you gain more points, you level up a medal as well.

Points	Medal
100	駆け出し収集家
1000	名の知れた収集家
4000	驚くべき収集家
7000	マスター収集家
10000	伝説の収集家

IF YOU READ NOTHING ELSE, AT LEAST READ THIS SECTION SO YOU WON'T BE CONFUSED WHEN YOU LOOK AT MONSTER BOOK SETS:
There are different sets of cards that you can collect. Collecting a whole set of cards grants you a special reward. The most noticeable reward is additional exp, which ranges from 65 EXP for the lowest set to 3.8m EXP for the highest set. Also, the more difficult of a set that you complete the better stats you gain on an item. The Monster Book data says which kind of potential stat you can receive. The level of your Monster Book determines the power of the potential stat.

Just a guess here, but let me give an example:

One of the higher sets, called 降魔の十字旅団, gives two potential stats. One potential stat is +All Stat%, and the other is Ignore Enemy Defense. The level of the potential stat is determined by the level of your Monster Book. So if your Monster Book is level 10, you will receive "Ignore 15% Target DEF" and "All Stat +3%". Given that these bonuses work just like potential bonuses, I would assume that they stack as potential bonuses stack.

The final bonus you get from a set is a "set score". I assume this adds to the total number of points for your Monster Book. There's a huge reward for collecting everything from one set, but it doesn't appear to be very easy to collect a few of the sets.

Monsterbook Sets

1 ﾋﾞｸﾄﾘｱｱｲﾗﾝﾄﾞの友達

ﾋﾞｸﾄﾘｱｱｲﾗﾝﾄﾞの友達
EXP: 65
Score: +10
Bonus: HP (Book Level*5)

2 リエンの友達

リエンの友達
EXP: 447
Score: +10
Bonus: +HP (Book Level*5)

3 エーデルシュタインの友達

エーデルシュタインの友達
EXP: 328
Score: +10
Bonus: +HP (Book Level*5)

4 カニングシティー

カニングシティー
EXP: 1818
Score: +30
Bonus: +Avoid (Book Level*2)

5 カニングスクエア

カニングスクエア
EXP: 6852
Score: +50
Bonus: +Avoid (Book Level*2)

6 エリニア

エリニア
EXP: 1893
Score: +40
Bonus: +MP (Book Level*5)

7 スリーピーウッド

スリーピーウッド
EXP: 39,333
Score: +90
Bonus: Weapon Attack / Weapon Defense (Book Level*5)

Level	WAttack
1/2	+1
3/4	+2
5/6	+3
7/8	+4
9/10	+5

8 ぺリオン

ぺリオン
EXP: 2481
Score: +40
Bonus: +HP (Book Level*5)

9 ヘネシス

ヘネシス
EXP: 1339
Score: +30
Bonus: +ACC (Book Level*2)

10 キノコの城

キノコの城
EXP: 3453
Score: +40
Bonus: +Jump

Levels	Jump
1/3	+1
4/7	+2
8/10	+3

11 海の見える街

海の見える街
EXP: 4860
Score: +50
Bonus: +Speed

Levels	Speed
1/3	+1
4/7	+2
8/10	+3

12 エーデルシュタイン

エーデルシュタイン
EXP: 2136
Score: +50
Bonus: +Weapon Defense (Book Level*5)

13 レーベン鉱山

レーベン鉱山
EXP: 80,388
Score: +55
Bonus: +Weapon Defense / Magic Defense (Book Level*5)

14 二ハル砂漠

二ハル砂漠
EXP: 44,478
Score: +90
Bonus: MP / Magic Defense (Book Level*5)

15 マガティア

マガティア
EXP: 86,015
Score: +110
Bonus: INT / Magic Atack

Levels	INT	M-Attack
1/2	+2	+1
3/4	+4	+2
5/6	+6	+3
7/8	+8	+4
9/10	+10	+5

16 ルディブリアム

ルディブリアム
EXP: 23,071
Score: +160
Bonus: +HP / Weapon Defense (Book Level*10)

17 時計塔の最下階

時計塔の最下階
EXP: 224,666
Score: +130
Bonus: +HP% / Weapon Defense (Book Level*5)

Levels	HP%
1/3	+1%
4/7	+2%
8/10	+3%

18 エリン森

エリン森
EXP: 36,759
Score: +90
Bonus: +HP / Weapon Defense (Book Level*5)

19 アクアロード

アクアロード
EXP: 114,948
Score: +240
Bonus: Magic Attack% / Magic Defense (Book Level*10)

Levels	M-Attack
1/3	+2%
4/7	+4%
8/10	+6%

20 オルビス

オルビス
EXP: 14,381
Score: +60
Bonus: Speed / Jump

Levels	Speed/Jump
1/3	+1
4/7	+2
8/10	+3

21 エルナス

エルナス
EXP: 12,330
Score: +60
Bonus: Weapon Attack / DEX

Levels	Weapon Attack/DEX
1/2	+1
3/4	+2
5/6	+3
7/8	+4
9/10	+5

22 閉鉱

閉鉱
EXP: 381,269
Score: +210
Bonus: Weapon Attack% / Magic Attack

Levels	W-Attack	M-Attack
1	+2%	2
2	+2%	2
3	+2%	4
4	+4%	4
5	+4%	6
6	+4%	6
7	+4%	8
8	+6%	8
9	+6%	10
10	+6%	10

23 地球防衛本部＆下町

地球防衛本部＆下町
EXP: 26,378
Score: +80
Bonus: INT / MP (Book Level*5)

Levels	INT
1/2	+1
3/4	+2
5/6	+3
7/8	+4
9/10	+5

24 武陵桃源

武陵桃源
EXP: 876,608
Score: +320
Bonus: Invincible (2% chance for ? seconds) / Ignore enemy's defense by 15% (always)

Levels	Seconds
1/4	5
5/8	6
9/10	7

25 ミナル

ミナル
EXP: 1,537,475
Score: +680
Bonus: All Skills +1 (always) / Increase meso drop probability by %

Levels	Probabilty
1/3	20%
4/7	30%
8/10	40%

26 時間の神殿

時間の神殿
EXP: 3,835,136
Score: +285
Bonus: HP Recover / MP Recover (both 3% chance)

Level	HP/MP Recover
1	20
2	23
3	26
4	29
5	32
6	35
7	38
8	41
9	44
10	47

27 キノコ神社

キノコ神社
EXP: 161,221
Score: +240
Bonus: MP Recover (15% chance) / Magic Defense %

Level	MP Recover	M-Defense
1	40	1%
2	45	1%
3	50	1%
4	55	2%
5	60	2%
6	65	2%
7	70	2%
8	75	3%
9	80	3%
10	85

28 忍者城

忍者城
EXP: 3,835,136
Score: +190
Bonus: Speed / Jump

Levels	Speed/Jump
1/3	+2
4/7	+4
8/10	+6

29 ショーワ町

ショーワ町
EXP: 3,275,242
Score: +180
Bonus: All Stats / Avoid +%

1	Level	All Stat	Avoid
2	1	+1	1%
3	2	+1	1%
4	3	+2	1%
5	4	+2	2%
6	5	+3	2%
7	6	+3	2%
8	7	+4	2%
9	8	+4	3%
10	9	+5	3%
11	10	+5	3%

30 未来東京&クリムゾンウッド

未来東京&クリムゾンウッド
EXP: 3,835,136
Score: +360
Bonus: Potion Efficiency% / HP%

Level	Potion	HP
1/3	10%	2%
4/7	20%	4%
8/10	30%	6%

31 上海

上海
EXP: 7661
Score: +60
Bonus: Weapon Attack / Weapon Defense (Book Level*5)

Levels	W-Attack
1/2	+1
3/4	+2
5/6	+3
7/8	+4
9/10	+5

32 少林寺

少林寺
EXP: 876,608
Score: +160
Bonus: STR / Weapon Attack

Levels	STR/W-Attack
1/2	+2
3/4	+4
5/6	+6
7/8	+8
9/10	+10

33 降魔の十字旅団

降魔の十字旅団
EXP: 211,327
Score: +240
Bonus: All Stats% / Ignore Defence 15% (always)

Levels	All Stats %
1/3	+1%
4/7	+2%
8/10	+3%