There are (at least) two ways to do this:
1. Via the clipboard
Select the records you want from a table in Manifold, Copy
From R read the data from the clipboard using read.delim the default separator is a tab, so it works already - but we can specify that and other options via arguments.
>d <- read.delim("clipboard")
"d" is now a data frame in R with all the data from the Manifold table. This works for virtual tables of images and surfaces, but it doesn't work for the binary geometry columns (you will get a text summary of those).
2. Using RODBC.
This option requires R with the RODBC package installed, get these from a CRAN mirror via http://www.r-project.org, and a function defined for connecting to a save Manifold project file (see below).
Open a connection to a .map file (I copied this from the function odbcConnectAccess)
>ch <- odbcConnectManifold("C:/temp/world.map")
Submit a query to the connection, and assign the results to variable "d"
>d <- sqlQuery(ch, "SELECT [Longitude (I)] AS lon, [Latitude (I)] AS lat, [Capital] AS name FROM [Countries] WHERE [Area (I)] > 150;")
(We convert the field names to sensible character strings for ease of use later).
"d" is now a data frame with the (centroid) location coordinates and city names of all objects from the "Countries" drawing in "world.map"
My original posting on Georeference, including the function required is here: