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Updates: 

Uruguay observed daylight saving time from 2004 to 2015, but it will be staying on standard time in summer 2015-2016.

The Instituto Nacional de Estatística has posted census results on its website. They are described as "Definitive Data from Census Phase I - 2004 (revised to 2005-04-25)". I wasn't able to find an "as of" date for the population data. As a result, I'm not sure whether the 2005-04-25 revision date represents population projections, or just the date when the INE finished tabulating the data.

Country overview: 

Short name	URUGUAY
ISO code	UY
FIPS code	UY
Language	Spanish (es)
Time zone	-3
Capital	Montevideo

 

Uruguay has been independent throughout the 20th century.

Other names of country: 

1. Danish: Uruguay
2. Dutch: Uruguay, Oostelijke Republiek Uruguay (formal)
3. English: Eastern Republic of Uruguay (formal)
4. Finnish: Uruguay
5. French: Uruguay m
6. German: Uruguay, Republik f Östlich des Uruguay n (formal)
7. Icelandic: Úrúgvæ
8. Italian: Uruguay m
9. Norwegian: Uruguay, Republikken Uruguay (formal)
10. Portuguese: Uruguai, República f Oriental do Uruguai m (formal)
11. Russian: Восточная Республика Уругвай (formal)
12. Spanish: Uruguay, República f Oriental del Uruguay m (formal)
13. Swedish: Uruguay
14. Turkish: Uruguay, Uruguay Doğu Cumhuriyeti (formal)

Origin of name: 

possibly from irugua: chief channel + y: river, or Guarani uru: bird, huguay: tail (one source interprets the name as "river of the beautifully colored birds")

Primary subdivisions: 

Uruguay is divided into nineteen departamentos (departments).

Department	HASC	FIPS	Population	Area(km.²)	Area(mi.²)	Capital	Pc
Artigas	UY.AR	UY01	73,378	11,928	4,605	Artigas	55
Canelones	UY.CA	UY02	520,187	4,536	1,751	Canelones	90
Cerro Largo	UY.CL	UY03	84,698	13,648	5,270	Melo	37
Colonia	UY.CO	UY04	123,203	6,106	2,358	Colonia (del Sacramento)	70
Durazno	UY.DU	UY05	57,088	11,643	4,495	Durazno	97
Flores	UY.FS	UY06	25,050	5,144	1,986	Trinidad	85
Florida	UY.FD	UY07	67,048	10,417	4,022	Florida	94
Lavalleja	UY.LA	UY08	58,815	10,016	3,867	Minas	30
Maldonado	UY.MA	UY09	164,300	4,793	1,851	Maldonado	20
Montevideo	UY.MO	UY10	1,319,108	530	205	Montevideo	10
Paysandú	UY.PA	UY11	113,124	13,922	5,375	Paysandú	60
Río Negro	UY.RN	UY12	54,765	9,282	3,584	Fray Bentos	65
Rivera	UY.RV	UY13	103,493	9,370	3,618	Rivera	40
Rocha	UY.RO	UY14	68,088	10,551	4,074	Rocha	27
Salto	UY.SA	UY15	124,878	14,163	5,468	Salto	50
San José	UY.SJ	UY16	108,309	4,992	1,927	San José (de Mayo)	80
Soriano	UY.SO	UY17	82,595	9,000	3,475	Mercedes	75
Tacuarembó	UY.TA	UY18	90,053	15,438	5,961	Tacuarembó	45
Treinta y Tres	UY.TT	UY19	48,134	9,529	3,679	Treinta y Tres	33
19 departments			3,286,314	175,008	67,571
HASC: Hierarchical administrative subdivision codes. If periods are replaced by hyphens, these are the same as the department codes from ISO standard 3166-2. FIPS: Codes from FIPS PUB 10-4. Population: 2011-09-01 census Capital: The informal name is the part not in parentheses. Pc: Uruguay uses five-digit códigos postales. The numbers given in the table are the first two digits for each department. Treinta y Tres was well chosen.

Territorial extent: 

The departments of Colonia, Flores, San José, and Soriano appear to meet in a single point.

The UN LOCODE page  for Uruguay lists locations in the country, some of them with their latitudes and longitudes, some with their ISO 3166-2 codes for their subdivisions. This information can be put together to approximate the territorial extent of subdivisions.

Origins of names: 

1. Artigas: From its capital city, named after José Gervasio Artigas (1764-1850), revolutionary leader.
2. Canelones: Spanish canelón, augmentative of canal: channel. Canelón Grande and Canelón Chico flow through the department.
3. Cerro Largo: Spanish cerro: hill, largo: long.
4. Colonia: From its capital city, Colonia del Sacramento, named for its colonial history.
5. Durazno: From its capital city, named for a strategic pass with a lone peach tree (Spanish durazno).
6. Flores: For General Venancio Flores (1808-1868).
7. Florida: From its capital city, originally (1809) named San Fernando de la Florida, after King Fernando VII of Spain and the Count of Florida Blanca.
8. Lavalleja: For Juan Antonio Lavalleja (1784-1853), commander of the 33 patriots.
9. Maldonado: After Lt. Francisco Maldonado, the local commander in 1530.
10. Montevideo: Spanish monte: mountain + Latin video: I see.
11. Paysandú: Possibly after missionary Policarpo Sandú, with Guaraní honorific paí.
12. Rivera: For General Fructuoso Rivera (1784-1854), first president of Uruguay.
13. Rocha: From its capital city, founded (1793) as Nuestra Señora de los Remedios de Rocha.
14. Salto: For a waterfall (Spanish salto) on the Uruguay River, since impounded
16. Soriano: From its capital city, founded (1793) as Santo Domingo Soriano
18. Tacuarembó: From the river of that name, from Guaraní tacuá: (sugar) cane, îrembó: sprout.
19. Treinta y Tres: Spanish for thirty-three, the number of patriots under Lavalleja who invaded from Buenos Aires, raised an army, and gained Uruguay's independence in 1825-1828.

Change history: 

1. 1828-08-27: Uruguay divided by law into nine departamentos (departments): Canelones, Cerro Largo, Colonia, Durazno, Maldonado, Montevideo, Paysandú, San José, and Soriano.
2. 1837-06-14: Minas department formed from parts of Cerro Largo and Maldonado; Salto and Tacuarembó departments split from Paysandú.
3. 1856-07-10: Florida department split from San José.
4. 1880-07-07: Río Negro department split from Paysandú; Rocha department split from Maldonado.
5. 1884-09-20: Treinta y Tres department split from Maldonado.
6. 1884-10-01: Artigas department split from Salto; Rivera department split from Tacuarembó.
7. 1885-12-30: Flores department split from San José.
8. 1927-12-22: Name of Minas department changed to Lavalleja.
9. Source: "Uruguay y su Espacio: antecedentes y una propuesta", by Bernardo Quagliotti de Bellis and Victor Chamorro, Editorial Geosur, 1979.

Other names of subdivisions: 

Montevideo: Montevidéu (Portuguese)

Population history:

The Web site of the Instituto Nacional de Estadística (INE) has population figures that differ slightly from those in "Administrative Subdivisions of Countries" (except for 1985, which agrees perfectly). I would take the INE figures to be more authoritative.

Department	1908	1911	1921?	1941	1953	1963-10-16	1975-05-21	1985-10-23	1996-05-22	2004-06-01	2011-09-01
Artigas	26,321	31,380	43,996	55,748	63,589	52,843	57,947	69,145	75,059	78,019	73,378
Canelones	87,874	97,719	132,862	199,232	201,359	258,195	325,594	364,248	443,053	485,240	520,187
Cerro Largo	44,742	49,307	66,092	96,488	110,339	71,023	74,027	78,416	82,510	86,564	84,698
Colonia	54,644	63,732	97,811	129,322	135,038	105,350	111,832	112,717	120,241	119,266	123,203
Durazno	42,325	47,253	64,226	94,291	99,063	53,635	55,699	55,077	55,716	58,859	57,088
Flores	16,082	19,030	28,014	35,835	35,565	23,530	24,745	24,739	25,030	25,104	25,050
Florida	45,406	51,202	72,315	105,932	106,284	63,987	67,129	66,474	66,503	68,181	67,048
Lavalleja	51,222	33,168	78,984	115,181	115,852	65,823	65,180	61,466	61,085	60,925	58,815
Maldonado	28,820	57,036	48,085	66,539	67,933	61,259	76,211	94,314	127,502	140,192	164,300
Montevideo	309,231	338,125	422,499	536,533	836,165	1,202,757	1,237,227	1,311,976	1,344,839	1,325,968	1,319,108
Paysandú	38,421	48,419	90,523	83,490	92,417	88,029	98,508	103,763	111,509	113,244	113,124
Río Negro	19,932	27,622	45,163	47,147	51,954	46,861	50,123	48,644	51,713	53,989	54,765
Rivera	35,683	39,413	52,442	74,746	91,740	77,086	82,043	89,475	98,472	104,921	103,493
Rocha	34,119	39,038	55,665	82,156	86,334	55,097	60,258	66,601	70,292	69,937	68,088
Salto	46,259	54,159	88,110	99,754	108,030	92,183	103,074	108,487	117,597	123,120	124,878
San José	46,324	51,785	69,759	97,301	96,848	79,563	88,000	89,893	96,664	103,104	108,309
Soriano	39,565	44,720	65,542	92,671	99,927	77,906	80,614	79,439	81,557	84,563	82,595
Tacuarembó	46,939	51,505	69,907	104,889	119,658	76,964	84,535	83,498	84,919	90,489	90,053
Treinta y Tres	28,777	32,897	48,219	68,371	72,063	43,419	45,683	46,869	49,502	49,318	48,134
Totals	1,042,686	1,177,510	1,640,214	2,185,626	2,590,158	2,595,510	2,788,429	2,955,241	3,163,763	3,241,003	3,286,314

Sources: 

1. Population 1908: Anuario Estadístico 1909.
2. Census 1911-12-31: The Statesman's Year-Book, 1913 edition.
3. Census 1921?: Rand McNally World Atlas, Commonwealth Edition, 1928, census date not given but must be before 1926.
4. Census 1941-1953: Official estimates.
5. Census 1963-2005: Census documents from INE.
6. [1] Quagliotti de Bellis, Bernardo, and Victor Chamorro, Uruguay y su Espacio: antecedentes y una propuesta. Editorial Geosur, 1979.
7. [2] Library of Congress country study  (retrieved 1999).
8. [3] Censos 2011 , Instituto Nacional de Estadística (retrieved 2012-08-18).