Update [08-04-2026]
It has passed 10 years by now since GW were detected from BHs merging.
The best way (or a very good way) to get acquainted with General Relativity is to get a hold of this books:

• The Meaning of Relativity - By A. Einstein (Fifth Edition)
  It has multiple chapters including: On geometry in general, Special Relativity, General Relativity, a first appendix with astronomical calculations, 2nd appendix with the Non-symmetric theory of relativity, Additional comments on each chapter
• RELATIVITY - The Special and the General Theory - A. EINSTEIN
  While the first edition was published in 1916, the author added several other chapters in the later editions including General Relativity and other areas it got experimental confirmation plus additional comments of unified field theory and astronomy
• Out of my later years - A. EINSTEIN
  This one has collected essays that were published during his lifetime on various philosophical things and science - (it has also a chapter describing again in simpler words the Einstein-Rosen bridge).

Here's also a list of papers Einstein wrote AFTER puting together the initial General Relativity theory (very useful, a must have for anyone going deep into GR and unified field theories - the base ground for any [sub]M-Theory & co. ):

• ANNALS OF MATHEMATICS Vol. 40, No. 4, October, 1939 - ON A STATIONARY SYSTEM WITH SPHERICAL SYMMETRY CONSISTING OF MANY GRAVITATING MASSES BY ALBERT EINSTEIN (Received May 10, 1939)
• ANNALS OF MATHEMATICS Vol. 39, No. 3, July, 1938 - ON A GENERALIZATION OF KALUZA'S THEORY OF ELECTRICITY BY A. EINSTEIN AND P. BERGMANN (Received April 8, 1938)
• ANNALS OF MATHEMATICS Vol. 44, No. 2, April, 1943 - ON THE NON-EXISTENCE OF REGULAR STATIONARY SOLUTIONS OF RELATIVISTIC FIELD EQUATIONS BY A. EINSTEIN AND WV. PAULI (Received January 4, 1943)
• The Particle Problem in the General Theory of Relativity A.Einstein and N.Rosen, Institude for Advanced Study, Princeton (Received May 8, 1935)
  (known for the initial description of the Einstein-Rosen bridge)
• ANNALS OF MATHEMATICS Vol. 39, No. 1, January, 1938 - THE GRAVITATIONAL EQUATIONS AND THE PROBLEM OF MOTION BY A. EINSTEIN, L. INFELD, AND B. HOFFMANN (Received June 16, 1937)
• ANNALS 0P MATHEMATICS Vol. 41, No. 2, April, 1940 - THE GRAVITATIONAL EQUATIONS AND THE PROBLEM OF MOTION. II BY A. EINSTEIN AND L. INFELD (Received May 29, 1939)
• ON THE MOTION OF PARTICLES IN THE GENERAL RELATIVITY THEORY - A. EINSTEIN and L. INFIELD (Received February 12, 1949)
• ANNALS OF MATHEMATICS Vol. 62, No. 1, July. 1955 Printed in U.S.A. - A NEW FORM OF THE GENERAL RELATIVISTIC FIELD EQUATIONS By A. EINSTEIN AND B. KAUFMAN (Received January 27, 1955)
• ANNALS OF MATHEMATICS Vol. 46, No. 4, October, 1945 - A GENERALIZATION OF THE RELATIVISTIC THEORY OF GRAVITATION BY ALBERT EINSTEIN (Received June 19, 1945)
• ANNALS OF MATHEMATICS Vol. 47, No. 4, October, 1946 - A GENERALIZATION OF THE RELATIVISTIC THEORY OF GRAVITATION, II By A. EINSTEIN AND E. G. STRAUS (Received January 24, 1946)

Update [11-02-2016]
So it's official as of today 11-feb-2016 ! Gravitational waves have been detected from 2 merging blackholes.
LIGO detected in 2 separate locations (north-west of USA) and (south-east of USA) this cosmic event on September 2015
But today the scientific community gave them the recognition they deserved
It has been 100years since Einstein first published some paperwork regarding GW but only know they have been acknowleged and detected properly
by the scientific community.
I was very confident in Einstein's findings... I still am in more other things. Hope one day they'll come true !
Thanks Einstein - again!
https://youtu.be/B4XzLDM3Py8

ds2 = gμνdxμdxν

Γαμν = 1/2 gατ(∂gμτ/∂xν + ∂gντ/∂xμ - ∂gμν/∂xτ)

δAα = - Γαμν Aμ dxν

dx2α/ds2 = - Γαμν dxμ/ds dxν/ds

ΔAα = ∮δAα

ΔAα = - ∮Γαμν Aμ dxν

ΔAμ = 1/2 Rμσαβ Aσ fαβ

Rμσαβ = -∂Γμσα/∂xβ + ∂Γμσβ/∂xα + ΓμραΓρσβ - ΓμρβΓρσα

Rμν = -∂Γαμν/∂xα + ΓαμβΓβνα + ∂Γαμα/∂xν - ΓαμνΓβαβ

R = gμν Rμν

fαβ = ∮(xαdxβ - xβdxα)


Rμν - 1/2 gμν R = -kTμν

Rμν = -k(Tμν - 1/2 gμνT) = -kT*μν