Coming to America (Second Edition): A History of Immigration and Ethnicity in American Life by Roger Daniels is a comprehensive survey of immigration to the United States. The 451 pages of text begin with Jamestown and end with the new millennium. Plus there more than 50 additional pages including pictures, three appendices, notes, a selected bibliography and an index. Don't let the size of the volume scare you away, as it is geared towards the general reader and student. This second edition only appears to differ from the first in that there is a new chapter at the end.
As with most surveys of this type, the bulk of the book focuses on emigration after 1820, there are only about 120 pages on the colonial era. Additionally, the only place where British emigrants are mentioned in the sections dealing with emigration after 1820 is on the page where Daniels says although he won't be talking about them one should not conclude that they weren't important. I have nine "sticky-tabs" indicating where Scots or the Scots-Irish are mentioned or sections about them begin - probably about 20 pages altogether.
I understand these decisions taken by Daniels - most emigrants came to the United States after 1820; emigrants from England, Scotland, Wales and Northern Ireland probably did have an easier time adjusting to the US than other groups; and more research has been done on English emigrants to Colonial American than other groups. However, since these are my special areas of interest, I wish they they would be more fully included in general surveys.
The books is organized into thirds: Part 1: Colonial America; Part 2: The Century of Immigration (1820-1924); and Part Three: Modern Times. Each section includes a brief history of the migration patterns and experience of several groups that came during a particular period, for example English or Scandinavians during the Colonial Period; Italians, Poles, Chinese or French Canadians during the the Century of Immigration; and Mexicans, Vietnamese or refugees from Communist regimes during Modern Times. Also included in each section are chapters detailing issues specific to each time period: ethnicity, nativism, and immigration law.
If you are looking for an introduction to the entirety of American Immigration History; a few pages on a specific immigrant group; or a refresher on the subject (which it was for me) this book would be a good choice. For those of you who wish to know more about a group or time period that is included this volume, the extensive notes and bibliography will provide many leads for further reading.