Interpreting Multiple Linear Regression Summary

I would appreciate pointers on what I should read to understand this
output:

  summary(lm(TDS ~ Cond + Ca + Cl + Mg + Na + SO4))

Call:
lm(formula = TDS ~ Cond + Ca + Cl + Mg + Na + SO4)

Residuals:
ALL 1 residuals are 0: no residual degrees of freedom!

Coefficients: (6 not defined because of singularities)
             Estimate Std. Error t value Pr(>|t|)
(Intercept)      125         NA      NA       NA
Cond              NA         NA      NA       NA
Ca                NA         NA      NA       NA
Cl                NA         NA      NA       NA
Mg                NA         NA      NA       NA
Na                NA         NA      NA       NA
SO4               NA         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
   (63 observations deleted due to missingness)

   When I look at the summary for the data frame used for this model I do
not
see an excessive number of missing values or indications why there are no
residual degrees of freedom. The same model applied to 8 other data frames
did not produce similar results.

Puzzled,

Rich