diff --git a/ExaArray/ExaArray2D.cs b/ExaArray/ExaArray2D.cs
new file mode 100644
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+++ b/ExaArray/ExaArray2D.cs
@@ -0,0 +1,76 @@
+using System;
+
+namespace Exa
+{
+    /// <summary>
+    /// The two-dimensional exa-scale array. Can grow up to 18,446,744,073,709,551,615 elements in total.
+    /// </summary>
+    public sealed class ExaArray2D<T>
+    {
+        /// <summary>
+        /// The total number of possible elements.
+        /// </summary>
+        public const ulong MAX_NUMBER_ELEMENTS = ulong.MaxValue;
+
+        private ulong sumLengthOrdinates = 0;
+        
+        // Chunk storage:
+        private ExaArray1D<ExaArray1D<T>> chunks = new ExaArray1D<ExaArray1D<T>>(Strategy.MAX_PERFORMANCE);
+        
+        /// <summary>
+        /// Returns the current total number of elements across all dimensions. 
+        /// </summary>
+        /// <remarks>
+        /// Performance: O(1)
+        /// </remarks>
+        public ulong Length => this.sumLengthOrdinates;
+
+        /// <summary>
+        /// Gets or sets an element of the array.
+        /// </summary>
+        /// <remarks>
+        /// Getting a value: When asking for elements which are not yet allocated, returns <c>default(T)</c>. Performance: O(1).
+        /// 
+        /// Setting a value: The underlying data structure gets extended on demand as necessary. The array can and will grow
+        /// on demand per index. For example, the abscissa index 5 might have allocated memory for 15 elements while abscissa
+        /// index 16 have allocated memory for 1,000 elements.
+        ///
+        /// Performance, when the memory is already allocated: O(1)
+        /// Performance to extend on demand: O(n)
+        ///
+        /// On the abscissa, you extend up to 1,152,921,504,606,850,000 entries. Across all dimensions, you can have 18,446,744,073,709,551,615
+        /// elements on total.
+        /// </remarks>
+        /// <exception cref="ArgumentOutOfRangeException">Throws, when you tried to extend more than 1,152,921,504,606,850,000 elements on the abscissa
+        /// or you tried to extend to more than 18,446,744,073,709,551,615 elements in total.</exception>
+        public T this[ulong indexAbscissa, ulong indexOrdinate]
+        {
+            get
+            {
+                if (indexAbscissa >= this.chunks.Length - 1 || indexOrdinate >= this.chunks[indexAbscissa]?.Length)
+                    return default(T);
+
+                return this.chunks[indexAbscissa][indexOrdinate];
+            }
+
+            set
+            {
+                if(indexAbscissa >= this.chunks.Length - 1)
+                    this.chunks.Extend(indexAbscissa - this.chunks.Length + 1);
+                
+                this.chunks[indexAbscissa] ??= new ExaArray1D<T>(Strategy.MAX_PERFORMANCE);
+                if(indexOrdinate >= this.chunks[indexAbscissa].Length - 1)
+                {
+                    var extendBy = indexOrdinate - this.chunks[indexAbscissa].Length + 1;
+                    if(extendBy > MAX_NUMBER_ELEMENTS - this.sumLengthOrdinates)
+                        throw new ArgumentOutOfRangeException($"It is not possible to extend more than {MAX_NUMBER_ELEMENTS} total elements across all dimensions.");
+                    
+                    this.chunks[indexAbscissa].Extend(extendBy);
+                    this.sumLengthOrdinates += extendBy;
+                }
+
+                this.chunks[indexAbscissa][indexOrdinate] = value;
+            }
+        }
+    }
+}
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