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

The barracks is the building in which new troops are created.

Upgrades to the barracks speeds up the rate at which new troops are made. Each successive level cumulatively reduces the training time of units by 10%.

Costs and time to build level 1:

 210 |  140 |  260 |  120 |  4 |   ?

Requirements:
Rally Point Level 1, Main Building Level 3

Units to build:
Gaul: Phalanx, Swordsman
Roman: Legionnaire, Praetorian, Imperian
Teuton: Clubswinger, Spearfighter, Axefighter, Scout

Level							Culture Points	Training Length
1	210	140	260	120	?	4	1	100%
2	270	180	335	155	?	2	1	90%
3	345	230	425	195	?	2	2	81%
4	440	295	545	250	?	2	2	73%
5	565	375	700	320	?	2	2	66%
6	720	480	895	410	?	3	3	59%
7	925	615	1145	530	?	3	4	53%
8	1180	790	1465	675	?	3	4	48%
9	1515	1010	1875	865	?	3	5	43%
10	1935	1290	2400	1105	?	3	6	39%
11	2480	1655	3070	1415	?	3	7	35%
12	3175	2115	3930	1815	?	3	9	31%
13	4060	2710	5030	2320	?	3	11	28%
14	5200	3465	6435	2970	?	3	13	25%
15	6655	4435	8240	3805	?	3	15	23%
16	8520	5680	10545	4870	?	4	18	21%
17	10905	7270	13500	6230	?	4	22	19%
18	13955	9305	17280	7975	?	4	27	17%
19	17865	11910	22120	10210	?	4	32	15%
20	22865	15245	28310	13065	?	4	38	14%

Final build times with Level 20 Barracks
Legionnaire - 0:04:30
Praetorian - 0:04:57
Imperian - 0:05:24
Phalanx - 0:02:56
Swordfighter - 0:04:03
Clubswinger - 0:02:02
Spearfighter - 0:03:09
Axefighter - 0:03:23
Scout - 0:03:09