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From Travian v2 Wiki (S2-S6), the encyclopedia anybody can edit

The Academy is the building in which new troops can be developed.

Upgrades to the academy, occasionally in conjunction with upgrades to other buildings, unlock the ability to research new types of units at the academy. Per example, in order to create Imperians, the Roman player would upgrade his Academy to level 5 and construct a Blacksmith; then visit the Academy and choose to research the Imperian. Once research is complete, the player can create Imperians at his Barracks.

To build an academy one must first upgrade the main building and the barracks to level 3.

Costs and time to build level 1:

 220 |  160 |  90 |  40 |  4 |  ?

Requirements for Level 1
Barracks Level 3, Main Building Level 3

Level							Culture Points
1	220	160	90	40	?	4	5
2	280	205	115	50	?	2	6
3	360	260	145	65	?	2	7
4	460	335	190	85	?	2	8
5	590	430	240	105	?	2	10
6	755	550	310	135	?	3	12
7	970	705	395	175	?	3	14
8	1240	900	505	225	?	3	17
9	1585	1155	650	290	?	3	21
10	2030	1475	830	370	?	3	25
11	2595	1890	1065	470	?	3	30
12	3325	2420	1360	605	?	3	36
13	4255	3095	1740	775	?	3	43
14	5445	3960	2230	990	?	3	51
15	6970	5070	2850	1270	?	3	62
16	8925	6490	3650	1625	?	4	74
17	11425	8310	4275	2075	?	4	89
18	14620	10635	5980	2660	?	4	106
19	18715	13610	7655	3405	?	4	128
20	23955	17420	9800	4355	?	4	153

Construction Times

Construction Period Based on Main Building (MB) Level - Levels 1-10

Academy Level	MB Level 1	MB Level 2	MB Level 3	MB Level 4	MB Level 5	MB Level 6	MB Level 7	MB Level 8	MB Level 9	MB Level 10
1	-	-	0:33:20	0:33:20	0:33:20	0:33:20	0:33:20	0:33:20	0:33:20	0:33:20
2	-	-	0:40:30	0:39:10	0:37:40	0:36:20	0:35:00	0:33:50	0:32:30	0:31:20
3	-	-	0:51:40	0:49:50	0:48:00	0:46:20	0:44:40	0:43:00	0:41:30	0:40:00
4	-	-	1:04:40	1:02:20	1:00:00	0:57:50	0:55:50	0:53:50	0:51:50	0:50:00
5	-	-	1:19:40	1:16:50	1:14:00	1:11:20	1:08:50	1:06:20	1:03:50	1:01:40
6	-	-	1:37:00	1:33:30	1:30:10	1:26:50	1:23:50	1:20:50	1:17:50	1:15:00
7	-	-	1:57:10	1:53:00	1:48:50	1:45:00	1:41:10	1:37:30	1:34:00	1:30:40
8	-	-	2:20:30	2:15:30	2:10:40	2:06:00	2:01:20	1:57:00	1:52:50	1:48:50
9	-	-	2:47:40	2:41:40	2:35:50	2:30:20	2:24:50	2:19:40	2:14:40	2:09:50
10	-	-	3:19:10	3:12:00	3:05:10	2:58:30	2:52:00	2:45:50	2:39:50	2:34:10
11	-	-	3:55:40	3:47:10	3:39:00	3:31:10	3:23:30	3:16:10	3:09:10	3:02:20
12	-	-	4:38:00	4:18:30	4:09:10	4:00:10	3:51:30	3:43:10	3:35:10
13	-	-	5:27:10	5:15:30	5:04:10	4:53:10	4:42:40	4:32:20	4:22:40	4:13:10
14	-	-	6:24:10	6:10:20	5:57:00	5:44:10	5:31:50	5:19:50	5:08:20	4:57:20
15	-	-	7:30:20	7:14:10	6:58:30	6:43:30	6:28:50	6:14:50	6:01:30	5:48:20
16	-	-	8:47:00	8:28:00	8:09:50	7:52:10	7:35:10	7:18:50	7:03:00	6:47:40
17	-	-	10:16:00	9:53:50	9:32:30	9:11:50	8:52:00	8:32:50	8:14:20	7:56:30
18	-	-	11:59:10	11:33:20	11:08:20	10:44:20	10:21:10	9:58:50	9:37:10	9:16:30
19	-	-	13:59:00	13:28:50	12:59:40	12:31:30	12:04:30	11:38:30	11:13:20	10:49:00
20	-	-	16:17:50	15:42:40	15:08:40	14:36:00	14:04:30	13:34:00	13:04:40	12:36:30

Construction Period Based on Main Building (MB) Level - Levels 11-20

Academy Level	MB Level 11	MB Level 12	MB Level 13	MB Level 14	MB Level 15	MB Level 16	MB Level 17	MB Level 18	MB Level 19	MB Level 20
1	0:33:20	0:33:20	0:33:20	0:33:20	0:33:20	0:33:20	0:33:20	0:33:20	0:33:20	0:33:20
2	0:30:20	0:29:10	0:28:10	0:27:10	0:26:10	0:25:10	0:24:20	0:23:20	0:22:30	0:21:50
3	0:38:30	0:37:10	0:35:50	0:34:30	0:33:20	0:32:10	0:31:00	0:29:50	0:28:50	0:27:40
4	0:48:10	0:46:30	0:44:50	0:43:10	0:41:40	0:40:10	0:38:40	0:37:20	0:36:00	0:34:40
5	0:59:20	0:57:10	0:55:10	0:53:10	0:51:20	0:49:30	0:47:40	0:46:00	0:44:20	0:42:40
6	1:12:20	1:09:40	1:07:10	1:04:50	1:02:30	1:00:10	0:58:00	0:56:00	0:54:00	0:52:00
7	1:27:20	1:24:10	1:21:10	1:18:20	1:15:30	1:12:50	1:10:10	1:07:40	1:05:10	1:02:50
8	1:44:50	1:41:00	1:37:30	1:34:00	1:30:30	1:27:20	1:24:10	1:21:10	1:18:10	1:15:20
9	2:05:10	2:00:30	1:56:10	1:52:00	1:48:00	1:44:10	1:40:20	1:36:50	1:33:20	1:30:00
10	2:28:30	2:23:10	2:18:00	2:13:10	2:08:20	2:03:40	1:59:10	1:55:00	1:50:50	1:46:50
11	2:55:50	2:49:30	2:43:20	2:37:30	2:31:50	2:26:20	2:21:10	2:16:00	2:11:10	2:06:20
12	3:27:20	3:20:00	3:12:40	3:05:50	2:59:10	2:52:40	2:46:30	2:40:30	2:34:40	2:29:10
13	4:04:00	3:55:20	3:46:50	3:38:40	3:30:40	3:23:10	3:15:50	3:08:50	3:02:00	2:55:30
14	4:46:30	4:36:10	4:26:20	4:16:40	4:07:30	3:58:30	3:50:00	3:41:40	3:33:40	3:26:00
15	5:35:50	5:23:50	5:12:10	5:00:50	4:50:00	4:39:40	4:29:30	4:19:50	4:10:30	4:01:30
16	6:33:00	6:19:00	6:05:20	5:52:10	5:39:30	5:27:10	5:15:30	5:04:10	4:53:10	4:42:40
17	7:39:30	7:22:50	7:07:00	6:51:30	6:36:50	6:22:30	6:08:40	5:55:30	5:42:40	5:30:20
18	8:56:20	8:37:10	8:18:30	8:00:30	7:43:10	7:26:30	7:10:30	6:55:00	6:40:00	6:25:40
19	10:25:40	10:03:10	9:41:30	9:20:30	9:00:20	8:40:50	8:22:10	8:04:00	7:46:40	7:29:50
20	12:09:20	11:43:00	11:17:40	10:53:20	10:29:50	10:07:10	9:45:20	9:24:10	9:03:50	8:44:20