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Here are the direct links for researching race and ethnicity in Indiana volumes of the U.S. Census.

A note about terminology - at the beginning of census race and ethnicity research, you'll find outdated terms. Today's Census Bureau works to be as current and accurate as possible to the terms people use to self-describe. However, terms used in the past, while not appropriate and even offensive, can show up in your research. 

I've gathered links to each year from 1830-1890 for you for easy access.

1830 Census: https://www.census.gov/programs-surveys/decennial-census/decade.1830.html

1840 Census: https://www.census.gov/programs-surveys/decennial-census/decade.1840.html

*1830 & 1840  Population Census volumes are not part of the Census Bureau's digital collection, but they may be available at a Federal Depository Library in your state. If you need these population figures for Indiana, please let me know and I'll arrange to scan pages for you from our volumes of reprints from 1830 and 1840.

1850 Census: https://www.census.gov/programs-surveys/decennial-census/decade.1850.html

     Full digitized volumes: https://www.census.gov/library/publications/1853/dec/1850a.html

     Indiana: https://www2.census.gov/library/publications/decennial/1850/1850a/1850a-42.pdf

     See "Classifications of Age and Color"

1860 Census: census.gov/programs-surveys/decennial-census/decade.1860.html

     Full digitized volumes: https://www.census.gov/library/publications/1864/dec/1860a.html

     Indiana: https://www2.census.gov/library/publications/decennial/1860/population/1860a-12.pdf

     p5 shows the aggregate of "White" "Free Colored" and "Indian"

1870 Census: https://www.census.gov/programs-surveys/decennial-census/decade.1870.html

     Full digitized volumes: https://www.census.gov/library/publications/1872/dec/1870a.html

     Indiana: https://www2.census.gov/library/publications/decennial/1870/population/1870a-15.pdf

1880 Census: https://www.census.gov/programs-surveys/decennial-census/decade.1880.html

     Full digitized volumes: https://www.census.gov/library/publications/1883/dec/vol-01-population.html

     Race and Ethnicity Tables, by state: 

     https://www2.census.gov/library/publications/decennial/1880/vol-01-population/1880_v1-13.pdf

1890 Census: https://www.census.gov/programs-surveys/decennial-census/decade.1890.html

     Full digitized volumes: https://www.census.gov/library/publications/1895/dec/volume-1.html

     Indiana (p24 of PDF): https://www2.census.gov/library/publications/decennial/1890/volume-1/1890a_v1-06.pdf

     Race and Ethnicity Tables by state: 

     https://www2.census.gov/library/publications/decennial/1890/volume-1/1890a_v1-13.pdf

     Foreign Born Population (p17 of PDF): https://www2.census.gov/library/publications/decennial/1890/volume-1/1890a_v1-16.pdf

1900 Census: https://www.census.gov/programs-surveys/decennial-census/decade/decennial-publications.1900.html

     Foreign Parentage (p77 of PDF): https://www2.census.gov/library/publications/decennial/1900/volume-1/volume-1-p3.pdf

          Foreign Parentage by Country (p84 of the PDF, Indiana is listed in North Central division)

          Citizenship and Years in the United States (p88 pf PDF)

     Sex, General Nativity and Color (p7 and p45 of PDF):

      (Indiana appears in almost all of these tables) 

       https://www2.census.gov/library/publications/decennial/1900/volume-1/volume-1-p10.pdf 

      (p7 and p45 of PDF) https://www2.census.gov/library/publications/decennial/1900/volume-1/volume-1-p11.pdf

     Country of Birth: (Indiana appears in all of these tables) 

      https://www2.census.gov/library/publications/decennial/1900/volume-1/volume-1-p13.pdf

    Foreign Parentage: (Indiana appears in most of these tables)

     https://www2.census.gov/library/publications/decennial/1900/volume-1/volume-1-p14.pdf

    Citizenship and Years in US: (Indiana appears in most of these tables)

     https://www2.census.gov/library/publications/decennial/1900/volume-1/volume-1-p15.pdf

1910 Census

     Color or Race, Nativity, and Parentage: (Indiana is listed in East North Central division)

          Indiana on pages 17, 24, 34, 35, 40, 46. You can scroll further down for county- and city-level race and ethnicity data. 

          Indiana on pages 67, 72, 74, 77. Scroll down further for counties and cities.

          https://www2.census.gov/library/publications/decennial/1910/volume-1/volume-1-p4.pdf

     Country of Birth of the Foreign Born Population

          Indiana on pages 27, 32, 34, 36, 37, 52, 56, 60, 61, 88. Scroll through for cities.

          https://www2.census.gov/library/publications/decennial/1910/volume-1/volume-1-p11.pdf

     Country of Origin of the Foreign White Stock

          Indiana on pages 19, 21, 26, 34, 44, 54, 64. Scroll down further for cities.

          https://www2.census.gov/library/publications/decennial/1910/volume-1/volume-1-p12.pdf

     Indiana volume (p83):

          Pages 109+ Scroll through for county and city/town-level data.

          https://www2.census.gov/library/publications/decennial/1910/volume-2/volume-2-p5.pdf

1920 Census: https://www.census.gov/programs-surveys/decennial-census/decade/decennial-publications.1920.html

     Indiana volume (p 79): Race and Ethnicity data on pages 80, 83, 86. Scroll down for city/town-level data.

     https://www2.census.gov/library/publications/decennial/1920/volume-3/41084484v3ch03.pdf     

1930 Census: https://www.census.gov/programs-surveys/decennial-census/decade/decennial-publications.1930.html

     Volume 2, Chapter 2: Indiana on pages 13-18, 20, 26, 32, 36, 39, 43, 44. Scroll down for city/town-level data.

     https://www2.census.gov/library/publications/decennial/1930/population-volume-2/16440598v2ch03.pdf

     Volume 2, Chapter 5: Indiana on pages 12-14, 21. Scroll down for city/town-level data.

     https://www2.census.gov/library/publications/decennial/1930/population-volume-2/16440598v2ch06.pdf

     Volume 2, Chapter 6: Indiana on pages 12-23, 33. Scroll down for city/town-level data.

     https://www2.census.gov/library/publications/decennial/1930/population-volume-2/16440598v2ch07.pdf

     Volume 2, Chapter 8: Indiana on pages 16, 17, 18-19, 20, 21, 22, 26, 36, 48, 53, 82.

     https://www2.census.gov/library/publications/decennial/1930/population-volume-2/16440598v2ch08.pdf

Additional 1930 Census figures on race and ethnicity broken down by state can be found in 3, 4, 5, and the supplement to Volume 6, all found here: https://www.census.gov/programs-surveys/decennial-census/decade/decennial-publications.1930.html